Mizar Mathematical Library (current wiki state)

[A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z]

A

ABCMIZ_0,

Grzegorz Bancerek. On semilattice structure of {M}izar types

ABCMIZ_1,

Grzegorz Bancerek. Towards the construction of a model of Mizar concepts

ABCMIZ_A,

Grzegorz Bancerek. A Model of Mizar Concepts -- Unification

ABIAN,

Piotr Rudnicki and Andrzej Trybulec. Abian's Fixed Point Theorem

ABSVALUE,

Jan Popio{\l}ek. Some Properties of Functions Modul and Signum

AFF_1,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Parallelity and Lines in Affine Spaces

AFF_2,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Classical Configurations in Affine Planes

AFF_3,

Eugeniusz Kusak, Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Affine Localizations of Desargues Axiom

AFF_4,

Wojciech Leo\'nczuk, Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Planes in Affine Spaces

AFINSQ_1,

Tetsuya Tsunetou , Grzegorz Bancerek and Yatsuka Nakamura. Zero Based Finite Sequences

AFINSQ_2,

Yatsuka Nakamura and Hisashi Ito. Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences

AFPROJ,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. A Projective Closure and Projective Horizon of an Affine Space

AFVECT0,

Grzegorz Lewandowski, Krzysztof Pra\.zmowski and Bo\.zena Lewandowska. Directed Geometrical Bundles and Their Analytical Representation

AFVECT01,

Barbara Konstanta, Urszula Kowieska, Grzegorz Lewandowski and. One-Dimensional Congruence of Segments, Basic Facts and Midpoint Relation

ALG_1,

Ma{\l}gorzata Korolkiewicz. Homomorphisms of algebras. Quotient Universal Algebra

ALGSEQ_1,

Micha{\l} Muzalewski and Les{\l}aw W. Szczerba. Construction of Finite Sequences over Ring and Left-, Right-, and Bi-Modules over a Ring

ALGSPEC1,

Grzegorz Bancerek. Technical Preliminaries to Algebraic Specifications

ALGSTR_0,

Library Committee. Basic Algebraic Structures

ALGSTR_1,

Micha{\l} Muzalewski and Wojciech Skaba. From Loops to Abelian Multiplicative Groups with Zero

ALGSTR_2,

Wojciech Skaba and Micha{\l} Muzalewski. From Double Loops to Fields

ALGSTR_3,

Micha{\l} Muzalewski and Wojciech Skaba. Ternary Fields

ALGSTR_4,

Marco Riccardi. Free Magmas

ALI2,

Alicia de la Cruz. Fix Point Theorem for Compact Spaces

ALTCAT_1,

Andrzej Trybulec. Categories without Uniqueness of { \bf cod } and { \bf dom }

ALTCAT_2,

Andrzej Trybulec. Examples of Category Structures.Subcategories

ALTCAT_3,

Beata Madras. Basic properties of objects and morphisms. In categories without uniqueness of { \bf cod } and { \bf dom }

ALTCAT_4,

Artur Korni{\l}owicz. On the Categories Without Uniqueness of { \bf cod } and { \bf dom } . Some Properties of the Morphisms and the Functors

AMI_1,

Yatsuka Nakamura and Andrzej Trybulec. A Mathematical Model of CPU

AMI_2,

Yatsuka Nakamura and Andrzej Trybulec. On a Mathematical Model of Programs

AMI_3,

Andrzej Trybulec and Yatsuka Nakamura. Some Remarks on Simple Concrete Model of Computer

AMI_4,

Andrzej Trybulec and Yatsuka Nakamura. Euclide Algorithm

AMI_5,

Yasushi Tanaka. On the Decomposition of the States of SCM

AMI_6,

Artur Korni{\l}owicz. On the Instructions of { \bf SCM }

AMI_WSTD,

Andrzej Trybulec , Piotr Rudnicki and Artur Korni{\l}owicz. Weakly Standard Ordering of Instruction Locations

AMISTD_1,

Andrzej Trybulec , Piotr Rudnicki and Artur Korni{\l}owicz. Standard Ordering of Instruction Locations

AMISTD_2,

Artur Korni{\l}owicz. On the Composition of Macro Instructions of Standard Computers

AMISTD_3,

Artur Korni{\l}owicz. A Tree of Execution of a Macroinstruction

AMISTD_4,

Artur Korni{\l}owicz. Input and Output of Instructions

AMISTD_5,

Andrzej Trybulec. Relocable Instructions

ANALMETR,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Analytical Metric Affine Spaces and Planes

ANALOAF,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Analytical Ordered Affine Spaces

ANALORT,

Jaroslaw Zajkowski. Oriented Metric-Affine Plane - Part I

ANPROJ_1,

Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski. A Construction of Analytical Projective Space

ANPROJ_2,

Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski. Projective Spaces

AOFA_000,

Grzegorz Bancerek. Mizar Analysis of Algorithms: Preliminaries

AOFA_I00,

Grzegorz Bancerek. Mizar Analysis of Algorithms: Algorithms over Integers

ARITHM,

Library Committee. Field Properties of Complex Numbers - Requirements

ARMSTRNG,

William W. Armstrong , Yatsuka Nakamura and Piotr Rudnicki. Armstrong's Axioms

ARROW,

Freek Wiedijk. Arrow's Impossibility Theorem

ARYTM_0,

Andrzej Trybulec. Introduction to Arithmetics

ARYTM_1,

Andrzej Trybulec. Non negative real numbers. Part II

ARYTM_2,

Andrzej Trybulec. Non negative real numbers. Part I

ARYTM_3,

Grzegorz Bancerek. Arithmetic of Non Negative Rational Numbers

ASYMPT_0,

Richard Krueger , Piotr Rudnicki and Paul Shelley. Asymptotic notation. Part I: Theory

ASYMPT_1,

Richard Krueger, Piotr Rudnicki and Paul Shelley. Asymptotic notation. Part II: Examples and Problems

AUTALG_1,

Artur Korni{\l}owicz. On the Group of Automorphisms of Universal Algebra & Many Sorted Algebra

AUTGROUP,

Artur Korni{\l}owicz. On the Group of Inner Automorphisms

AXIOMS,

Andrzej Trybulec. Strong arithmetic of real numbers

B

BAGORDER,

Gilbert Lee and Piotr Rudnicki. On Ordering of Bags

BCIALG_1,

Yuzhong Ding. Several Classes of {BCI}-algebras and Their Properties

BCIALG_2,

Yuzhong Ding and Zhiyong Pang. Congruences and Quotient Algebras of {BCI}-algebras

BCIALG_3,

Tao Sun , Dahai Hu and Xiquan Liang. Several Classes of {BCK}-algebras and Their Properties

BCIALG_4,

Tao Sun , Junjie Zhao and Xiquan Liang. BCI-Algebras with Condition (S) and Their Properties

BCIALG_5,

Tao Sun , Weibo Pan , Chenglong Wu and Xiquan Liang. General Theory of Quasi-Commutative BCI-algebras

BCIALG_6,

Yuzhong Ding , Fuguo Ge and Chenglong Wu. {BCI}-Homomorphisms

BCIIDEAL,

Chenglong Wu and Yuzhong Ding. Ideals of BCI-Algebras and Their Properties

BHSP_1,

Jan Popio{\l}ek. Introduction to Banach and Hilbert spaces - Part I

BHSP_2,

Jan Popio{\l}ek. Introduction to Banach and Hilbert spaces - Part II

BHSP_3,

Jan Popio{\l}ek. Introduction to Banach and Hilbert spaces - Part III

BHSP_4,

El\.zbieta Kraszewska and Jan Popio{\l}ek. Series in Banach and Hilbert Spaces

BHSP_5,

Hiroshi Yamazaki , Yasunari Shidama and Yatsuka Nakamura. Bessel's Inequality

BHSP_6,

Hiroshi Yamazaki , Yasumasa Suzuki , Takao Inou\'e and Yasunari Shidama. On Some Properties of Real {H}ilbert Space, {I}

BHSP_7,

Hiroshi Yamazaki , Yasumasa Suzuki , Takao Inou\'e and Yasunari Shidama. On Some Properties of Real {H}ilbert Space, {II}

BILINEAR,

Jaros{\l}aw Kotowicz. Bilinear Functionals in Vector Spaces

BINARI_2,

Yasuho Mizuhara and Takaya Nishiyama. Binary Arithmetics. Addition and Subtraction of Integers

BINARI_3,

Robert Milewski. Binary Arithmetics. Binary Sequences

BINARI_4,

Hisayoshi Kunimune and Yatsuka Nakamura. A Representation of Integers by Binary Arithmetics and Addition of Integers

BINARITH,

Takaya Nishiyama and Yasuho Mizuhara. Binary Arithmetics. Addition

BINOM,

Christoph Schwarzweller. The Binomial Theorem for Algebraic Structures

BINOP_1,

Czes{\l}aw Byli\'nski. Binary Operations

BINOP_2,

Library Committee. Binary Operations on Numbers

BINTREE1,

Grzegorz Bancerek and Piotr Rudnicki. On Defining Functions on Binary Trees

BINTREE2,

Robert Milewski. Full Trees

BIRKHOFF,

Artur Korni{\l}owicz. Birkhoff Theorem for Many Sorted Algebras

BOOLE,

Library Committee. Boolean Properties of Sets - Requirements

BOOLEALG,

Agnieszka Julia Marasik. Boolean Properties of Lattices

BOOLMARK,

Pauline N. Kawamoto, Yasushi Fuwa and Yatsuka Nakamura. Basic Concepts for Petri Nets with Boolean Markings. Boolean Markings and the Firability/Firing of Transitions

BOR_CANT,

Peter Jaeger. Borel-Cantelli Lemma

BORSUK_1,

Andrzej Trybulec. A Borsuk Theorem on Homotopy Types

BORSUK_2,

Adam Grabowski. Introduction to Homotopy Theory

BORSUK_3,

Adam Grabowski. Properties of the Product of Compact Topological Spaces

BORSUK_4,

Adam Grabowski. On the Decompositions of Intervals and Simple Closed Curves

BORSUK_5,

Adam Grabowski. On the Subcontinua of a Real Line

BORSUK_6,

Adam Grabowski and Artur Korni{\l}owicz. Algebraic Properties of Homotopies

BROUWER,

Artur Korni{\l}owicz and Yasunari Shidama. Brouwer Fixed Point Theorem for Disks on the Plane

BROUWER2,

Karol P\kak. Brouwer Fixed Point Theorem in the General Case

BSPACE,

Jesse Alama. The Vector Space of Subsets of a Set Based on Symmetric Difference

BVFUNC10,

Shunichi Kobayashi. Propositional Calculus for Boolean Valued Functions, VI

BVFUNC11,

Shunichi Kobayashi and Yatsuka Nakamura. Predicate Calculus for Boolean Valued Functions, III

BVFUNC14,

Shunichi Kobayashi. Predicate Calculus for Boolean Valued Functions, { VI }

BVFUNC25,

Shunichi Kobayashi. Propositional Calculus for Boolean Valued Functions, {VII }

BVFUNC26,

Shunichi Kobayashi. Propositional Calculus for Boolean Valued Functions, {VIII}

BVFUNC_1,

Shunichi Kobayashi and Kui Jia. A Theory of Boolean Valued Functions and Partitions

BVFUNC_2,

Shunichi Kobayashi and Yatsuka Nakamura. A Theory of Boolean Valued Functions and Quantifiers with Respect to Partitions

BVFUNC_3,

Shunichi Kobayashi and Yatsuka Nakamura. Predicate Calculus for Boolean Valued Functions, { I }

BVFUNC_4,

Shunichi Kobayashi and Yatsuka Nakamura. Predicate Calculus for Boolean Valued Functions, II

BVFUNC_5,

Shunichi Kobayashi and Yatsuka Nakamura. Propositional Calculus for Boolean Valued Functions, I

BVFUNC_6,

Shunichi Kobayashi and Yatsuka Nakamura. Propositional Calculus for Boolean Valued Functions, II

BVFUNC_7,

Shunichi Kobayashi. Propositional Calculus For Boolean Valued Functions, III

BVFUNC_8,

Shunichi Kobayashi. Propositional Calculus For Boolean Valued Functions, IV

BVFUNC_9,

Shunichi Kobayashi. Propositional Calculus for Boolean Valued Functions, { V }

C

C0SP1,

Yasunari Shidama , Hikofumi Suzuki and Noboru Endou. Banach Algebra of Bounded Functionals

C0SP2,

Katuhiko Kanazashi, Noboru Endou and Yasunari Shidama. Banach Algebra of Continuous Functionals and Space of Real-valued Continuous Functionals with Bounded Support

CALCUL_1,

Patrick Braselmann and Peter Koepke. A Sequent Calculus for First-Order Logic

CALCUL_2,

Patrick Braselmann and Peter Koepke. Consequences of the Sequent Calculus

CANTOR_1,

Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor Set

CARD_1,

Grzegorz Bancerek. Cardinal Numbers

CARD_2,

Grzegorz Bancerek. Cardinal Arithmetics

CARD_3,

Grzegorz Bancerek. K\"onig's Theorem

CARD_4,

Grzegorz Bancerek. Countable Sets and Hessenberg's Theorem

CARD_5,

Grzegorz Bancerek. On Powers of Cardinals

CARD_FIL,

Josef Urban. Basic facts about inaccessible and measurable cardinals

CARD_FIN,

Karol P\c{a}k. Cardinal Numbers and Finite Sets

CARD_LAR,

Josef Urban. Mahlo and inaccessible cardinals

CARDFIN2,

Cezary Kaliszyk. Counting Derangements, Counting Non Bijective Functions and the Birthday Problem

CAT_1,

Czes{\l}aw Byli\'nski. Introduction to Categories and Functors

CAT_2,

Czes{\l}aw Byli\'nski. Subcategories and Products of Categories

CAT_3,

Czes{\l}aw Byli\'nski. Products and Coproducts in Categories

CAT_4,

Czes{\l}aw Byli\'nski. Cartesian Categories

CAT_5,

Grzegorz Bancerek. Categorial Categories and Slice Categories

CATALAN1,

Dorota Cz\c{e}stochowska and Adam Grabowski. Catalan Numbers

CATALAN2,

Karol P\c{a}k. The {C}atalan Numbers. {P}art {II}

CATALG_1,

Grzegorz Bancerek. Algebra of Morphisms

CAYLEY,

Artur Korni{\l}owicz. Cayley's Theorem

CC0SP1,

Katuhiko Kanazashi , Hiroyuki Okazaki and Yasunari Shidama. Banach Algebra of Bounded Complex-Valued Functionals

CFCONT_1,

Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama. Property of Complex Sequence and Continuity of Complex Function

CFDIFF_1,

Chanapat Pacharapokin , Hiroshi Yamazaki , Yasunari Shidama and Yatsuka Nakamura. Complex Function Differentiability

CFDIFF_2,

Hiroshi Yamazaki , Yasunari Shidama , Chanapat Pacharapokin and Yatsuka Nakamura. Cauchy-Riemann Differential Equations of Complex Functions

CFUNCDOM,

Noboru Endou. Complex Valued Function's Space

CFUNCT_1,

Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama. Property of Complex Functions

CGAMES_1,

Robin Nittka. Conway's Games and Some of Their Basic Properties

CHAIN_1,

Freek Wiedijk. Chains on a Grating in Euclidean Space

CHORD,

Broderick Arneson and Piotr Rudnicki. Chordal Graphs

CIRCCMB2,

Grzegorz Bancerek , Shin'nosuke Yamaguchi and Yasunari Shidama. Combining of Multi Cell Circuits

CIRCCMB3,

Grzegorz Bancerek and Adam Naumowicz. Preliminaries to Automatic Generation of Mizar Documentation for Circuits

CIRCCOMB,

Yatsuka Nakamura and Grzegorz Bancerek. Combining of Circuits

CIRCLED1,

Fahui Zhai , Jianbing Cao and Xiquan Liang. Circled Sets, Circled Hull, and Circled Family

CIRCTRM1,

Grzegorz Bancerek. Circuit Generated by Terms and Circuit Calculating Terms

CIRCUIT1,

Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec and Pauline N. Kawamoto. Introduction to Circuits, I

CIRCUIT2,

Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec and Pauline N. Kawamoto. Introduction to Circuits, II

CLASSES1,

Grzegorz Bancerek. Tarski's Classes and Ranks

CLASSES2,

Bogdan Nowak and Grzegorz Bancerek. Universal Classes

CLOPBAN1,

Noboru Endou. Complex {B}anach Space of Bounded Linear Operators

CLOPBAN2,

Noboru Endou. Banach Algebra of Bounded Complex Linear Operators

CLOPBAN3,

Noboru Endou. Series on Complex {B}anach Algebra

CLOPBAN4,

Noboru Endou. Exponential Function on Complex {B}anach Algebra

CLOSURE1,

Artur Korni{\l}owicz. On the Many Sorted Closure Operator and the Many Sorted Closure System

CLOSURE2,

Artur Korni{\l}owicz. On the Closure Operator and the Closure System of Many Sorted Sets

CLOSURE3,

Agnieszka Julia Marasik. Algebraic Operation on Subsets of Many Sorted Sets

CLVECT_1,

Noboru Endou. Complex Linear Space and Complex Normed Space

CLVECT_2,

Noboru Endou. Convergent Sequences in Complex Unitary Space

CLVECT_3,

Yasumasa Suzuki and Noboru Endou. Cauchy Sequence of Complex Unitary Space

COH_SP,

Jaros{\l}aw Kotowicz and Konrad Raczkowski. Coherent Space

COHSP_1,

Grzegorz Bancerek. Continuous, Stable, and Linear Maps of Coherence Spaces

COLLSP,

Wojciech Skaba. The Collinearity Structure

COMBGRAS,

Andrzej Owsiejczuk. Combinatorial {G}rassmannians

COMMACAT,

Grzegorz Bancerek and Agata Darmochwa\l. Comma Category

COMPACT1,

Czeslaw Bylinski. Alexandroff One Point Compactification

COMPL_SP,

Karol P\c{a}k. Complete Spaces

COMPLEX1,

Czes{\l}aw Byli\'nski. The Complex Numbers

COMPLEX2,

Wenpai Chang, Yatsuka Nakamura and Piotr Rudnicki. Inner Products and Angles of Complex Numbers

COMPLFLD,

Anna Justyna Milewska. The Field of Complex Numbers

COMPLSP1,

Czes{\l}aw Byli\'nski and Andrzej Trybulec. Complex Spaces

COMPLSP2,

Wenpai Chang , Hiroshi Yamazaki and Yatsuka Nakamura. The Inner Product and Conjugate of Finite Sequences of Complex Numbers

COMPOS_1,

Andrzej Trybulec. Composition of Machines, Instructions and Programs

COMPTRIG,

Robert Milewski. Trigonometric Form of Complex Numbers

COMPTS_1,

Agata Darmochwa{\l}. Compact Spaces

COMPUT_1,

Grzegorz Bancerek and Piotr Rudnicki. The set of primitive recursive functions

COMSEQ_1,

Agnieszka Banachowicz and Anna Winnicka. Complex Sequences

COMSEQ_2,

Adam Naumowicz. Conjugate Sequences, Bounded Complex Sequences and Convergent Complex Sequences

COMSEQ_3,

Yasunari Shidama and Artur Korni{\l}owicz. Convergence and the Limit of Complex Sequences. Series

CONAFFM,

Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski. Metric-Affine Configurations in Metric Affine Planes - Part I

CONLAT_1,

Christoph Schwarzweller. Introduction to Concept Lattices

CONLAT_2,

Christoph Schwarzweller. A Characterization of Concept Lattices; Dual Concept Lattices

CONMETR,

Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski. Metric-Affine Configurations in Metric Affine Planes - Part II

CONMETR1,

Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski. Shear Theorems and Their Role in Affine Geometry

CONNSP_1,

Beata Padlewska. Connected Spaces

CONNSP_2,

Beata Padlewska. Locally Connected Spaces

CONNSP_3,

Yatsuka Nakamura and Andrzej Trybulec. Components and Unions of Components

CONVEX1,

Noboru Endou , Takashi Mitsuishi and Yasunari Shidama. Convex Sets and Convex Combinations

CONVEX2,

Noboru Endou , Yasumasa Suzuki and Yasunari Shidama. Some Properties for Convex Combinations

CONVEX3,

Noboru Endou and Yasunari Shidama. Convex Hull, Set of Convex Combinations and Convex Cone

CONVEX4,

Hidenori Matsuzaki , Noboru Endou and Yasunari Shidama. Convex Sets and Convex Combinations on Complex Linear Spaces

CONVFUN1,

Grigory E. Ivanov. Definition of Convex Function and {J}ensen's Inequality

CQC_LANG,

Czes{\l}aw Byli\'nski. A Classical First Order Language

CQC_SIM1,

Agata Darmochwa{\l} and Andrzej Trybulec. Similarity of Formulae

CQC_THE1,

Agata Darmochwa{\l}. A First-Order Predicate Calculus. Axiomatics, the Consequence Operation and a Concept of Proof

CQC_THE2,

Agata Darmochwa\l. Calculus of Quantifiers. Deduction Theorem

CQC_THE3,

Oleg Okhotnikov. Logical Equivalence of Formulae

CSSPACE,

Noboru Endou. Complex Linear Space of Complex Sequences

CSSPACE2,

Noboru Endou. Hilbert Space of Complex Sequences

CSSPACE3,

Noboru Endou. Banach Space of Absolute Summable Complex Sequences

CSSPACE4,

Noboru Endou. Complex Banach Space of Bounded Complex Sequences

D

DECOMP_1,

Marian Przemski. On the Decomposition of the Continuity

DICKSON,

Gilbert Lee and Piotr Rudnicki. Dickson's lemma

DIFF_1,

Bo Li , Yan Zhang and Xiquan Liang. Difference and Difference Quotient

DIFF_2,

Bo Li , Yanping Zhuang and Xiquan Liang. Difference and Difference Quotient -- Part {II}

DIFF_3,

Xiquan Liang and Ling Tang. Difference and Difference Quotient -- Part {III}

DIFF_4,

Xiquan Liang , Ling Tang and Xichun Jiang. Difference and Difference Quotient -- Part {IV}

DILWORTH,

Piotr Rudnicki. Dilworth's Decomposition Theorem for Posets

DIRAF,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Ordered Affine Spaces Defined in Terms of Directed Parallelity - part I

DIRORT,

Jaros{\l}aw Zajkowski. Oriented Metric-Affine Plane - Part II

DIST_1,

Hiroyuki Okazaki. Probability on Finite and Discrete Set and Uniform Distribution

DOMAIN_1,

Andrzej Trybulec. Domains and Their Cartesian Products

DTCONSTR,

Grzegorz Bancerek and Piotr Rudnicki. On Defining Functions on Trees

DYNKIN,

Franz Merkl. Dynkin's Lemma in Measure Theory

E

E_SIEC,

Waldemar Korczy\'nski. Definitions of Petri Net - Part II

EC_PF_1,

Yuichi Futa , Hiroyuki Okazaki and Yasunari Shidama. Set of Points on Elliptic Curve in Projective Coordinates

ENDALG,

Jaros{\l}aw Gryko. On the Monoid of Endomorphisms of Universal Algebra \& Many Sorted Algebra

ENS_1,

Czes{\l}aw Byli\'nski. Category Ens

ENTROPY1,

Bo Zhang and Yatsuka Nakamura. Definition and Some Properties of Information Entropy

ENUMSET1,

Andrzej Trybulec. Enumerated Sets

EQREL_1,

Konrad Raczkowski and Pawe{\l} Sadowski. Equivalence Relations and Classes of Abstraction

EQUATION,

Artur Korni{\l}owicz. Equations in Many Sorted Algebras

EUCLID,

Agata Darmochwa{\l}. The Euclidean Space

EUCLID_2,

Kanchun and Yatsuka Nakamura. The Inner Product of Finite Sequences and of Points of $n$-dimensional Topological Space

EUCLID_3,

Akihiro Kubo and Yatsuka Nakamura. Angle and Triangle in {E}uclidian Topological Space

EUCLID_4,

Akihiro Kubo. Lines in $n$-Dimensional Euclidean Spaces

EUCLID_5,

Kanchun, Hiroshi Yamazaki and Yatsuka Nakamura. Cross Products and Tripple Vector Products in 3-dimensional Euclidian Space

EUCLID_6,

Marco Riccardi. Heron's Formula and Ptolemy's Theorem

EUCLID_7,

Yatsuka Nakamura , Artur Korni{\l}owicz , Nagato Oya and Yasunari Shidama. The Real Vector Spaces of Finite Sequences Are Finite Dimensional

EUCLID_8,

Xiquan Liang , Piqing Zhao and Ou Bai. Vector Function and its Differentiation Formulas in 3-dimensional Euclidean Spaces

EUCLID_9,

Artur Korni{\l}owicz. The Correspondence Between $n$-dimensional {E}uclidean Space and the Product of $n$ Real Lines

EUCLIDLP,

Akihiro Kubo. Lines on Planes in $n$-Dimensional Euclidean Spaces

EUCLMETR,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Fundamental Types of Metric Affine Spaces

EULER_1,

Yoshinori Fujisawa and Yasushi Fuwa. Euler's Function

EULER_2,

Yoshinori Fujisawa , Yasushi Fuwa and Hidetaka Shimizu. Euler's {T}heorem and Small {F}ermat's Theorem

EXCHSORT,

Grzegorz Bancerek. Sorting by Exchanging

EXTENS_1,

Artur Korni{\l}owicz. Extensions of Mappings on Generator Set

EXTPRO_1,

Yatsuka Nakamura and Andrzej Trybulec. Externally Programmed Machines

EXTREAL1,

Noboru Endou , Katsumi Wasaki and Yasunari Shidama. Basic Properties of Extended Real Numbers

EXTREAL2,

Noboru Endou , Katsumi Wasaki and Yasunari Shidama. Some Properties of Extended Real Numbers Operations: absolute value, min and max

F

FACIRC_1,

Grzegorz Bancerek and Yatsuka Nakamura. Full Adder Circuit. Part { I }

FACIRC_2,

Grzegorz Bancerek , Shin'nosuke Yamaguchi and Katsumi Wasaki. Full Adder Circuit. Part { II }

FCONT_1,

Konrad Raczkowski and Pawe{\l} Sadowski. Real Function Continuity

FCONT_2,

Jaros{\l}aw Kotowicz and Konrad Raczkowski. Real Function Uniform Continuity

FCONT_3,

Jaros{\l}aw Kotowicz. Monotonic and Continuous Real Function

FDIFF_1,

Konrad Raczkowski and Pawe{\l} Sadowski. Real Function Differentiability

FDIFF_10,

Bo Li and Pan Wang. Several Differentiation Formulas of Special Functions -- Part {V}

FDIFF_11,

Fuguo Ge and Bing Xie. Several Differentiation Formulas of Special Functions -- Part {VII}

FDIFF_2,

Jaros{\l}aw Kotowicz and Konrad Raczkowski. Real Function Differentiability - Part II

FDIFF_3,

Ewa Burakowska and Beata Madras. Real Function One-Side Differantiability

FDIFF_4,

Yan Zhang and Xiquan Liang. Several Differentiable Formulas of Special Functions

FDIFF_5,

Jianbing Cao , Fahui Zhai and Xiquan Liang. Some Differentiable Formulas of Special Functions

FDIFF_6,

Yan Zhang , Bo Li and Xiquan Liang. Several Differentiable Formulas of Special Functions -- Part {II}

FDIFF_7,

Bo Li , Yan Zhang and Xiquan Liang. Several Differentiation Formulas of Special Functions -- Part {III}

FDIFF_8,

Bo Li and Peng Wang. Several Differentiation Formulas of Special Functions -- Part {IV}

FDIFF_9,

Peng Wang and Bo Li. Several Differentiation Formulas of Special Functions -- Part {V}

FF_SIEC,

Waldemar Korczy\'nski. Definitions of Petri Net - Part I

FIB_FUSC,

Grzegorz Bancerek and Piotr Rudnicki. Two Programs for {\bf SCM}. Part II - Proofs

FIB_NUM,

Robert M. Solovay. Fibonacci Numbers

FIB_NUM2,

Magdalena Jastrz\c{e}bska and Adam Grabowski. Some Properties of {F}ibonacci Numbers

FIB_NUM3,

Piotr Wojtecki and Adam Grabowski. Lucas Numbers and Generalized {F}ibonacci Numbers

FIB_NUM4,

Magdalena Jastrz\c{e}bska. Representation of the {F}ibonacci and {L}ucas Numbers in Terms of the Floor and Ceiling Functor

FILEREC1,

Hirofumi Fukura and Yatsuka Nakamura. A Theory of Sequential Files

FILTER_0,

Grzegorz Bancerek. Filters - Part I. Implicative Lattices

FILTER_1,

Grzegorz Bancerek. Filters - Part II. Quotient Lattices Modulo Filters and Direct Product of Two Lattices

FILTER_2,

Grzegorz Bancerek. Ideals

FIN_TOPO,

Hiroshi Imura and Masayoshi Eguchi. Finite Topological Spaces. Finite Topology Concepts and Neighbourhoods

FINSEQ_1,

Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of Natural Numbers and Finite Sequences

FINSEQ_2,

Czes{\l}aw Byli\'nski. Finite Sequences and Tuples of Elements of a Non-empty Sets

FINSEQ_3,

Wojciech A. Trybulec. Non-contiguous Substrings and One-to-one Finite Sequences

FINSEQ_4,

Wojciech A. Trybulec. Pigeon Hole Principle

FINSEQ_5,

Czes\law Byli\'nski. Some Properties of Restrictions of Finite Sequences

FINSEQ_6,

Andrzej Trybulec. On the Decomposition of Finite Sequences

FINSEQ_7,

Hiroshi Yamazaki , Yoshinori Fujisawa and Yatsuka Nakamura. On Replace Function and Swap Function for Finite Sequences

FINSEQ_8,

Hirofumi Fukura and Yatsuka Nakamura. Concatenation of Finite Sequences Reducing Overlapping Part and an Argument of Separators of Sequential Files

FINSEQOP,

Czes{\l}aw Byli\'nski. Binary Operations Applied to Finite Sequences

FINSET_1,

Agata Darmochwa\l. Finite Sets

FINSOP_1,

Wojciech A. Trybulec. Binary Operations on Finite Sequences

FINSUB_1,

Andrzej Trybulec and Agata Darmochwa\l. Boolean Domains

FINTOPO2,

Gang Liu , Yasushi Fuwa and Masayoshi Eguchi. Formal topological spaces

FINTOPO3,

Masami Tanaka and Yatsuka Nakamura. Some Set Series in Finite Topological Spaces. {F}undamental Concepts for Image Processing

FINTOPO4,

Hiroshi Imura , Masami Tanaka and Yatsuka Nakamura. Continuous Mappings between Finite and One-Dimensional Finite Topological Spaces

FINTOPO5,

Masami Tanaka , Hiroshi Imura and Yatsuka Nakamura. Homeomorphism between Finite Topological Spaces, Two-Dimensional Lattice Spaces and a Fixed Point Theorem

FINTOPO6,

Yatsuka Nakamura. Connectedness and Continuous Sequences in Finite Topological Spaces

FLANG_1,

Micha{\l} Trybulec. Formal Languages -- Concatenation and Closure

FLANG_2,

Micha{\l} Trybulec. Regular Expression Quantifiers -- $m$ to $n$ Occurrences

FLANG_3,

Micha{\l} Trybulec. Regular Expression Quantifiers -- at least $m$ Occurrences

FOMODEL0,

Marco B. Caminati. Preliminaries to Classical First-order Model Theory

FOMODEL1,

Marco B. Caminati. Definition of first order language with arbitrary alphabet. Syntax of terms, atomic formulas and their subterms.

FOMODEL2,

Marco B. Caminati. First order languages: syntax, part two; semantics.

FOMODEL3,

Marco B. Caminati. Free interpretation, quotient interpretation and substitution of a letter with a term for first order languages.

FOMODEL4,

Marco B. Caminati. Sequent calculus, derivability, provability. Goedel's completeness theorem.

FOO,

Article Author. Article Title

FOO2,

Article Author. Article Title

FRAENKEL,

Andrzej Trybulec. Function Domains and Fr{\ae}nkel Operator

FRECHET,

Bart{\l}omiej Skorulski. First-countable, Sequential, and { F } rechet Spaces

FRECHET2,

Bart{\l}omiej Skorulski. The Sequential Closure Operator In Sequential and Frechet Spaces

FREEALG,

Beata Perkowska. Free Universal Algebra Construction

FSCIRC_1,

Katsumi Wasaki and Noboru Endou. Full Subtracter Circuit. Part { I }

FSCIRC_2,

Shin'nosuke Yamaguchi , Grzegorz Bancerek and Katsumi Wasaki. Full Subtracter Circuit. Part {II}

FSM_1,

Miroslava Kaloper and Piotr Rudnicki. Minimization of finite state machines

FSM_2,

Hisayoshi Kunimune , Grzegorz Bancerek and Yatsuka Nakamura. On state machines of calculating type

FSM_3,

Micha{\l} Trybulec. Equivalence of Epsilon, Nondeterministic [Finite] Automata and Deterministic [Finite] Automata

FTACELL1,

Katsumi Wasaki. Stability of the 4-2 Binary Addition Circuit Cells. Part {I}

FUNCOP_1,

Andrzej Trybulec. Binary Operations Applied to Functions

FUNCSDOM,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Real Functions Spaces

FUNCT_1,

Czes{\l}aw Byli\'nski. Functions and Their Basic Properties

FUNCT_2,

Czes{\l}aw Byli\'nski. Functions from a Set to a Set

FUNCT_3,

Czes{\l}aw Byli\'nski. Basic Functions and Operations on Functions

FUNCT_4,

Czes{\l}aw Byli\'nski. The Modification of a Function by a Function and the Iteration of the Composition of a Function

FUNCT_5,

Grzegorz Bancerek. Curried and Uncurried Functions

FUNCT_6,

Grzegorz Bancerek. Cartesian Product of Functions

FUNCT_7,

Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous Facts about Functions

FUNCT_8,

Bo Li and Yanhong Men. Basic properties of even and odd functions

FUNCT_9,

Bo Li , Yanhong Men , Dailu Li and Xiquan Liang. Basic Properties of Periodic Functions

FUNCTOR0,

Andrzej Trybulec. Functors for Alternative Categories

FUNCTOR1,

Claus Zinn and Wolfgang Jaksch. Basic Properties of Functor Structures

FUNCTOR2,

Robert Nieszczerzewski. Category of Functors between Alternative Categories

FUNCTOR3,

Artur Korni{\l}owicz. The Composition of Functors and Transformations in Alternative Categories

FUZZY_1,

Takashi Mitsuishi , Noboru Endou and Yasunari Shidama. Concept of Fuzzy Set and Membership Function and Basic Properties of Fuzzy Set Operation

FUZZY_2,

Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama. Basic Properties of Fuzzy Set Operation and Membership Function

FUZZY_4,

Noboru Endou , Takashi Mitsuishi and Keiji Ohkubo. Properties of Fuzzy Relation

FVSUM_1,

Katarzyna Zawadzka. Sum and Product of Finite Sequences of Elements of a Field

G

GATE_1,

Yatsuka Nakamura. Logic Gates and Logical Equivalence of Adders

GATE_2,

Yuguang Yang , Wasaki Katsumi , Yasushi Fuwa and Yatsuka Nakamura. Correctness of Binary Counter Circuits

GATE_3,

Yuguang Yang , Wasaki Katsumi , Yasushi Fuwa and Yatsuka Nakamura. Correctness of Johnson Counter Circuits

GATE_4,

Yuguang Yang , Katsumi Wasaki , Yasushi Fuwa and Yatsuka Nakamura. Correctness of a Cyclic Redundancy Check Code Generator

GATE_5,

Hiroshi Yamazaki and Katsumi Wasaki. Correctness of the High Speed Array Multiplier Circuits

GCD_1,

Christoph Schwarzweller. The correctness of the Generic Algorithms of Brown and Henrici concerning Addition and Multiplication in Fraction Fields

GENEALG1,

Akihiko Uchibori and Noboru Endou. Basic Properties of Genetic Algorithm

GEOMTRAP,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. A Construction of Analytical Ordered Trapezium Spaces

GFACIRC1,

Shin'nosuke Yamaguchi , Katsumi Wasaki and Nobuhiro Shimoi. Generalized Full Adder Circuits (GFAs). {P}art {I}

GFACIRC2,

Katsumi Wasaki. Stability of n-bit Generalized Full Adder Circuits (GFAs). Part {II}

GLIB_000,

Gilbert Lee and Piotr Rudnicki. Alternative Graph Structures

GLIB_001,

Gilbert Lee. Walks in a Graph

GLIB_002,

Gilbert Lee. Trees: Connected, Acyclic Graphs

GLIB_003,

Gilbert Lee. Weighted and Labeled Graphs

GLIB_004,

Gilbert Lee and Piotr Rudnicki. Proof of Dijkstra's Shortest Path Algorithm & Prim's Minimum Spanning Tree Algorithm

GLIB_005,

Gilbert Lee. Proof of Ford/Fulkerson's Maximum Network Flow Algorithm

GOBOARD1,

Jaros{\l}aw Kotowicz and Yatsuka Nakamura. Introduction to Go-Board - Part I. Basic Notations

GOBOARD2,

Jaros{\l}aw Kotowicz and Yatsuka Nakamura. Introduction to Go-Board - Part II. Go-Board Determined by Finite Sequence of point from ${\calE}^2_{\rm T}$

GOBOARD3,

Jaros{\l}aw Kotowicz and Yatsuka Nakamura. Properties of Go-Board - Part III

GOBOARD4,

Jaros{\l}aw Kotowicz and Yatsuka Nakamura. Go-Board Theorem

GOBOARD5,

Yatsuka Nakamura and Andrzej Trybulec. Decomposing a Go Board into Cells

GOBOARD6,

Andrzej Trybulec. On the Geometry of a Go-board

GOBOARD7,

Andrzej Trybulec. On the Go Board of a Standard Special Circular Sequence

GOBOARD8,

Andrzej Trybulec. More on Segments on a Go Board

GOBOARD9,

Andrzej Trybulec. Left and Right Component of the Complement of a Special Closed Curve

GOBRD10,

Yatsuka Nakamura and Andrzej Trybulec. Adjacency Concept for Pairs of Natural Numbers

GOBRD11,

Yatsuka Nakamura and Andrzej Trybulec. Some Topological Properties of Cells in $R^2$

GOBRD12,

Yatsuka Nakamura and Andrzej Trybulec. The First Part of Jordan's Theorem for Special Polygons

GOBRD13,

Czes{\l}aw Byli\'nski. Some Properties of Cells on Go Board

GOBRD14,

Artur Korni{\l}owicz. Properties of Left-, and Right Components

GOEDELCP,

Patrick Braselmann and Peter Koepke. G{\"o}del's Completeness Theorem

GR_CY_1,

Dariusz Surowik. Cyclic Groups and Some of Their Properties - Part I

GR_CY_2,

Dariusz Surowik. Isomorphisms of Cyclic Groups. Some Properties of Cyclic Groups

GR_CY_3,

Kenichi Arai and Hiroyuki Okazaki. Properties of Primes and Multiplicative Group of a Field

GRAPH_1,

Krzysztof Hryniewiecki. Graphs

GRAPH_2,

Yatsuka Nakamura and Piotr Rudnicki. Vertex sequences induced by chains

GRAPH_3,

Yatsuka Nakamura and Piotr Rudnicki. Euler circuits and paths

GRAPH_4,

Yatsuka Nakamura and Piotr Rudnicki. Oriented Simple Chains Included in Oriented Chains

GRAPH_5,

Jingchao Chen and Yatsuka Nakamura. The Underlying Principle of {D}ijkstra's Shortest Path Algorithm

GRAPHSP,

Jing-Chao Chen. Dijkstra's Shortest Path Algorithm

GRCAT_1,

Michal Muzalewski. Categories of Groups

GRFUNC_1,

Czes{\l}aw Byli\'nski. Graphs of Functions

GRNILP_1,

Dailu Li , Xiquan Liang and Yanhong Men. Nilpotent Groups

GROEB_1,

Christoph Schwarzweller. Characterization and Existence of {G}r\"obner Bases

GROEB_2,

Christoph Schwarzweller. Construction of {G}r\"obner bases. S-Polynomials and Standard Representations

GROEB_3,

Christoph Schwarzweller. Construction of {G}r\"obner Bases: Avoiding S-Polynomials -- Buchberger's First Criterium

GROUP_1,

Wojciech A. Trybulec. Groups

GROUP_10,

Marco Riccardi. The Sylow Theorems

GROUP_11,

Xiquan Liang and Dailu Li. On Rough Subgroup of a Group

GROUP_12,

Hiroyuki Okazaki , Kenichi Arai and Yasunari Shidama. Normal Subgroup of Product of Groups

GROUP_2,

Wojciech A. Trybulec. Subgroup and Cosets of Subgroups. Lagrange theorem

GROUP_3,

Wojciech A. Trybulec. Classes of Conjugation. Normal Subgroups

GROUP_4,

Wojciech A. Trybulec. Lattice of Subgroups of a Group. Frattini Subgroup

GROUP_5,

Wojciech A. Trybulec. Commutator and Center of a Group

GROUP_6,

Wojciech A. Trybulec and Micha{\l} J. Trybulec. Homomorphisms and Isomorphisms of Groups. Quotient Group

GROUP_7,

Artur Korni{\l}owicz. The Product of the Families of the Groups

GROUP_8,

Gijs Geleijnse and Grzegorz Bancerek. Properties of Groups

GROUP_9,

Marco Riccardi. The {J}ordan-H\"older Theorem

GROUPP_1,

Xiquan Liang and Dailu Li. Some Properties of $p$-Groups and Commutative $p$-Groups

GRSOLV_1,

Katarzyna Zawadzka. Solvable Groups

H

HAHNBAN,

Bogdan Nowak and Andrzej Trybulec. Hahn Banach Theorem

HAHNBAN1,

Anna Justyna Milewska. Hahn Banach Theorem in the Vector Space over the Field of Complex Numbers

HALLMAR1,

Ewa Romanowicz and Adam Grabowski. The {H}all {M}arriage {T}heorem

HAUSDORF,

Adam Grabowski. On the {H}ausdorff Distance Between Compact Subsets

HEINE,

Agata Darmochwa{\l} and Yatsuka Nakamura. Heine--Borel's Covering Theorem

HELLY,

Jessica Enright and Piotr Rudnicki. Helly property for subtrees

HENMODEL,

Patrick Braselmann and Peter Koepke. Equivalences of Inconsistency and {H}enkin Models

HERMITAN,

Jaros{\l}aw Kotowicz. Hermitan Functionals. {C}anonical Construction of Scalar Product in Quotient Vector Space

HESSENBE,

Eugeniusz Kusak and Wojciech Leo\'nczuk. Hessenberg Theorem

HEYTING1,

Andrzej Trybulec. Algebra of Normal Forms Is a Heyting Algebra

HEYTING2,

Adam Grabowski. Lattice of Substitutions Is a Heyting Algebra

HEYTING3,

Adam Grabowski. The Incompleteness of the Lattice of Substitutions

HFDIFF_1,

Junjie Zhao , Xiquan Liang and Li Yan. Several Higher Differentiation Formulas of Special Functions

HIDDEN,

.

HILBASIS,

Jonathan Backer and Piotr Rudnicki. Hilbert Basis Theorem

HILBERT1,

Adam Grabowski. Hilbert Positive Propositional Calculus

HILBERT2,

Andrzej Trybulec. Defining by structural induction in the positive propositional language

HILBERT3,

Andrzej Trybulec. The canonical formulae

HOLDER_1,

Yasumasa Suzuki. H\"older's Inequality and {M}inkowski's Inequality

HOMOTHET,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Homotheties and Shears in Affine Planes

HURWITZ,

Agnieszka Rowi\'nska-Schwarzweller and Christoph Schwarzweller. Schur's Theorem on the Stability of Networks

I

IDEA_1,

Yasushi Fuwa and Yoshinori Fujisawa. Algebraic group on Fixed-length bit integer and its adaptation to {IDEA} Cryptography

IDEAL_1,

Jonathan Backer , Piotr Rudnicki and Christoph Schwarzweller. Ring Ideals

INCPROJ,

Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski. Incidence Projective Spaces

INCSP_1,

Wojciech A. Trybulec. Axioms of Incidence

INDEX_1,

Grzegorz Bancerek. Indexed Category

INSTALG1,

Grzegorz Bancerek. Institution of Many-sorted Algebras, Part { I } : Signature Reduct of an Algebra

INT_1,

Micha{\l} J. Trybulec. Integers

INT_2,

Rafa{\l} Kwiatek and Grzegorz Zwara. The Divisibility of Integers and Integer Relatively Primes

INT_3,

Christoph Schwarzweller. The Ring of Integers, Euclidean Rings and Modulo Integers

INT_4,

Xiquan Liang , Li Yan and Junjie Zhao. Linear Congruence Relation and Complete Residue Systems

INT_5,

Li Yan , Xiquan Liang and Junjie Zhao. Gauss Lemma and Law of Quadratic Reciprocity

INT_6,

Christoph Schwarzweller. Modular Integer Arithmetic

INT_7,

Hiroyuki Okazaki and Yasunari Shidama. Uniqueness of factoring an integer and multiplicative group $Z/pZ^{*}$

INTEGR10,

Masahiko Yamazaki , Hiroshi Yamazaki , Yasunari Shidama and Yatsuka Nakamura. Extended {R}iemann Integral of Functions of Real Variable and One-sided {L}aplace Transform

INTEGR11,

Bo Li , Yanping Zhuang , Yanhong Men and Xiquan Liang. Several Integrability Formulas of Special Functions -- Part {II}

INTEGR12,

Bo Li and Na Ma. Integrability Formulas -- Part {I}

INTEGR13,

Bo Li , Na Ma and Xiquan Liang. Integrability Formulas -- Part {II}

INTEGR14,

Bo Li and Na Ma. Integrability Formulas -- Part {III}

INTEGR15,

Keiichi Miyajima and Yasunari Shidama. Riemann Integral of Functions $\mathbbbR$ into $\mathbbbR^n$

INTEGR16,

Keiichi Miyajima , Takahiro Kato and Yasunari Shidama. Riemann Integral of Functions $\mathbbbR$ into $\mathbbbC$

INTEGR18,

Keiichi Miyajima , Takahiro Kato and Yasunari Shidama. Riemann Integral of Functions from $\mathbbbR$ into Real Normed Space

INTEGR1C,

Masahiko Yamazaki , Hiroshi Yamazaki , Katsumi Wasaki and Yasunari Shidama. Complex Integral

INTEGRA1,

Noboru Endou and Artur Korni{\l}owicz. The Definition of Riemann Definite Integral and some Related Lemmas

INTEGRA2,

Noboru Endou , Katsumi Wasaki and Yasunari Shidama. Scalar Multiple of Riemann Definite Integral

INTEGRA3,

Noboru Endou , Katsumi Wasaki and Yasunari Shidama. Darboux's Theorem

INTEGRA4,

Noboru Endou , Katsumi Wasaki and Yasunari Shidama. Integrability of Bounded Total Functions

INTEGRA5,

Noboru Endou , Katsumi Wasaki and Yasunari Shidama. Definition of Integrability for Partial Functions from REAL to REAL and Integrability for Continuous Functions

INTEGRA6,

Noboru Endou , Yasunari Shidama and Masahiko Yamazaki. Integrability and the Integral of Partial Functions from $\Bbb R$ into $\Bbb R$

INTEGRA7,

Yasunari Shidama , Noboru Endou , Katsumi Wasaki and Katuhiko Kanazashi. Riemann Indefinite Integral of Functions of Real Variable

INTEGRA8,

Cuiying Peng , Fuguo Ge and Xiquan Liang. Several Integrability Formulas of Special Functions

INTEGRA9,

Bo Li , Yanping Zhuang , Bing Xie and Pan Wang. Several Integrability Formulas of Some Functions, Orthogonal Polynomials and Norm Functions

INTERVA1,

Adam Grabowski and Magdalena Jastrz\c{e}bska. On the Lattice of Intervals and Rough Sets

INTPRO_1,

Takao Inou\'e. Intuitionistic Propositional Calculus in the Extended Framework with Modal Operator, Part I

IRRAT_1,

Freek Wiedijk. Irrationality of e

ISOCAT_1,

Andrzej Trybulec. Isomorphisms of Categories

ISOCAT_2,

Andrzej Trybulec. Some Isomorphisms Between Functor Categories

ISOMICHI,

Magdalena Jastrz\c{e}bska and Adam Grabowski. The Properties of Supercondensed Sets, Subcondensed Sets and Condensed Sets

J

JCT_MISC,

Andrzej Trybulec. Miscellaneous { I }

JGRAPH_1,

Yatsuka Nakamura. Graph Theoretical Properties of Arcs in the Plane and Fashoda Meet Theorem

JGRAPH_2,

Yatsuka Nakamura. On Outside Fashoda Meet Theorem

JGRAPH_3,

Yatsuka Nakamura. On the Simple Closed Curve Property of the Circle and the Fashoda Meet Theorem for It

JGRAPH_4,

Yatsuka Nakamura. Fan Homeomorphisms in the Plane

JGRAPH_5,

Yatsuka Nakamura. General {F}ashoda {M}eet {T}heorem for Unit Circle

JGRAPH_6,

Yatsuka Nakamura. General {F}ashoda Meet Theorem for Unit Circle and Square

JGRAPH_7,

Yatsuka Nakamura and Andrzej Trybulec. Fashoda Meet Theorem for Rectangles

JGRAPH_8,

Yatsuka Nakamura , Andrzej Trybulec and Artur Korni{\l}owicz. The {F}ashoda Meet Theorem for Continuous Mappings

JORDAN,

Artur Korni{\l}owicz. Jordan's Curve Theorem

JORDAN1,

Yatsuka Nakamura and Jaros{\l}aw Kotowicz. The Jordan's Property for Certain Subsets of the Plane

JORDAN10,

Artur Korni{\l}owicz. Properties of the External Approximation of Jordan's Curve

JORDAN11,

Andrzej Trybulec. Preparing the Internal Approximations of Simple Closed Curves

JORDAN12,

Mariusz Giero. On the General Position of Special Polygons

JORDAN13,

Andrzej Trybulec. Introducing Spans

JORDAN14,

Robert Milewski. Properties of the Internal Approximation of {J}ordan's Curve

JORDAN15,

Robert Milewski. Properties of the Upper and Lower Sequence on the Cage

JORDAN16,

Andrzej Trybulec and Yatsuka Nakamura. On the Decomposition of a Simple Closed Curve into Two Arcs

JORDAN17,

Artur Korni{\l}owicz. The Ordering of Points on a Curve, Part {III}

JORDAN18,

Artur Korni{\l}owicz. The Ordering of Points on a Curve, Part {IV}

JORDAN19,

Robert Milewski. On the Upper and Lower Approximations of the Curve

JORDAN1A,

Artur Korni{\l}owicz, Robert Milewski, Adam Naumowicz and. Gauges and Cages

JORDAN1B,

Robert Milewski , Andrzej Trybulec , Artur Korni{\l}owicz. Some Properties of Cells and Arcs

JORDAN1C,

Adam Grabowski , Artur Korni{\l}owicz and Andrzej Trybulec. Some Properties of Cells and Gauges

JORDAN1D,

Artur Korni{\l}owicz and Robert Milewski. Gauges and Cages. { P } art { II }

JORDAN1E,

Robert Milewski. Upper and Lower Sequence of a Cage

JORDAN1F,

Adam Naumowicz. Some Remarks on Finite Sequences on Go-boards

JORDAN1G,

Robert Milewski. Upper and Lower Sequence on the Cage. Part II

JORDAN1H,

Andrzej Trybulec. More on External Approximation of a Continuum

JORDAN1I,

Adam Naumowicz and Robert Milewski. Some Remarks on Clockwise Oriented Sequences on Go-boards

JORDAN1J,

Robert Milewski. Upper and Lower Sequence on the Cage, Upper and Lower Arcs

JORDAN1K,

Andrzej Trybulec. On the Minimal Distance Between Set in {E}uclidean Space

JORDAN20,

Yatsuka Nakamura. Behaviour of an Arc Crossing a Line

JORDAN21,

Artur Korni{\l}owicz. On Some Points of a Simple Closed Curve

JORDAN22,

Artur Korni{\l}owicz and Adam Grabowski. On Some Points of a Simple Closed Curve. {P}art {II}

JORDAN23,

Robert Milewski. Subsequences of Almost, Weakly and Poorly One-to-one Finite Sequences

JORDAN24,

Adam Naumowicz and Grzegorz Bancerek. Homeomorphisms of {J}ordan Curves

JORDAN2B,

Roman Matuszewski and Yatsuka Nakamura. Projections in n-Dimensional Euclidean Space to Each Coordinates

JORDAN2C,

Yatsuka Nakamura , Andrzej Trybulec and Czeslaw Bylinski. Bounded Domains and Unbounded Domains

JORDAN3,

Yatsuka Nakamura and Roman Matuszewski. Reconstructions of Special Sequences

JORDAN4,

Yatsuka Nakamura , Roman Matuszewski and Adam Grabowski. Subsequences of Standard Special Circular Sequences in $ { \cal E } ^2_ { \rm T } $

JORDAN5A,

Adam Grabowski and Yatsuka Nakamura. Some Properties of Real Maps

JORDAN5B,

Adam Grabowski and Yatsuka Nakamura. The Ordering of Points on a Curve, Part { I }

JORDAN5C,

Adam Grabowski and Yatsuka Nakamura. The Ordering of Points on a Curve, Part { II }

JORDAN5D,

Yatsuka Nakamura and Adam Grabowski. Bounding Boxes for Special Sequences in ${\calE}^2$

JORDAN6,

Yatsuka Nakamura and Andrzej Trybulec. A Decomposition of Simple Closed Curves and an Order of Their Points

JORDAN7,

Yatsuka Nakamura. On a Dividing Function of the Simple Closed Curve into Segments

JORDAN8,

Czes\law Byli\'nski. Gauges

JORDAN9,

Czes{\l}aw Byli\'nski and Mariusz \.Zynel. Cages, external approximation of Jordan's curve

JORDAN_A,

Andrzej Trybulec. On the Segmentation of a Simple Closed Curve

K

KNASTER,

Piotr Rudnicki and Andrzej Trybulec. Fix-points in complete lattices

KOLMOG01,

Agnes Doll. Kolmogorov's Zero-one Law

KURATO_1,

Lilla Krystyna Bagi\'nska and Adam Grabowski. On the {K}uratowski Closure-Complement Problem

KURATO_2,

Adam Grabowski. On the {K}uratowski Limit Operators

L

L_HOSPIT,

Ma{\l}gorzata Korolkiewicz. The de l'Hospital Theorem

LANG1,

Patricia L. Carlson and Grzegorz Bancerek. Context-Free Grammar - Part 1

LAPLACE,

Karol P\c{a}k and Andrzej Trybulec. Laplace Expansion

LATSUBGR,

Janusz Ganczarski. On the Lattice of Subgroups of a Group

LATSUM_1,

Katarzyna Romanowicz and Adam Grabowski. The Operation of Addition of Relational Structures

LATTICE2,

Andrzej Trybulec. Finite Join and Finite Meet, and Dual Lattices

LATTICE3,

Grzegorz Bancerek. Complete Lattices

LATTICE4,

Jolanta Kamie\'nska and Jaros\l aw Stanis\l aw Walijewski. Homomorphisms of Lattices \\ Finite Join and Finite Meet

LATTICE5,

Jaros{\l}aw Gryko. J\'onsson Theorem

LATTICE6,

Christoph Schwarzweller. Noetherian Lattices

LATTICE7,

Marek Dudzicz. Representation Theorem For Finite Distributive Lattices

LATTICE8,

Mariusz {\L}api\'nski. J\'onsson Theorem about Representation of Modular Lattices

LATTICES,

Stanis{\l}aw \.Zukowski. Introduction to Lattice Theory

LEXBFS,

Broderick Arneson and Piotr Rudnicki. Recognizing Chordal Graphs: Lex BFS and MCS

LFUZZY_0,

Takashi Mitsuishi and Grzegorz Bancerek. Lattice of Fuzzy Sets

LFUZZY_1,

Takashi Mitsuishi and Grzegorz Bancerek. Transitive Closure of Fuzzy Relations

LIMFUNC1,

Jaros{\l}aw Kotowicz. The Limit of a Real Function at Infinity. Halflines. Real Sequence Divergent to Infinity

LIMFUNC2,

Jaros{\l}aw Kotowicz. One-Side Limits of a Real Function at a Point

LIMFUNC3,

Jaros{\l}aw Kotowicz. The Limit of a Real Function at a Point

LIMFUNC4,

Jaros{\l}aw Kotowicz. The Limit of a Composition of Real Functions

LMOD_5,

Micha{\l} Muzalewski and Wojciech Skaba. Linear Independence in Left Module over Domain

LMOD_6,

Micha{\l} Muzalewski. Submodules

LMOD_7,

Micha{\l} Muzalewski. Domains of Submodules, Join and Meet of Finite Sequences of Submodules and Quotient Modules

LOPBAN_1,

Yasunari Shidama. Banach Space of Bounded Linear Operators

LOPBAN_2,

Yasunari Shidama. The {B}anach Algebra of Bounded Linear Operators

LOPBAN_3,

Yasunari Shidama. The Series on {B}anach Algebra

LOPBAN_4,

Yasunari Shidama. The Exponential Function on {B}anach Algebra

LOPBAN_5,

Hideki Sakurai , Hisayoshi Kunimune and Yasunari Shidama. Uniform Boundedness Principle

LOPBAN_6,

Hideki Sakurai , Hisayoshi Kunimune and Yasunari Shidama. Open Mapping Theorem

LOPCLSET,

Jaros{\l}aw Stanis{\l}aw Walijewski. Representation Theorem for Boolean Algebras

LP_SPACE,

Yasumasa Suzuki. The Banach Space $l^p$

LPSPACE1,

Yasushige Watase , Noboru Endou and Yasunari Shidama. On $L^1$ Space Formed by Real-valued Partial Functions

LPSPACE2,

Yasushige Watase , Noboru Endou and Yasunari Shidama. On $L^p$ Space Formed by Real-valued Partial Functions

LTLAXIO1,

Mariusz Giero. The Axiomatization of Propositional Linear Time Temporal Logic

LUKASI_1,

Grzegorz Bancerek, Agata Darmochwa\l and Andrzej Trybulec. Propositional Calculus

M

MARGREL1,

Edmund Woronowicz. Many-Argument Relations

MATHMORP,

Yuzhong Ding and Xiquan Liang. Preliminaries to Mathematical Morphology and Its Properties

MATRIX10,

Xiquan Liang , Fuguo Ge and Xiaopeng Yue. Some Special Matrices of Real Elements and Their Properties

MATRIX11,

Karol P\c{a}k. Basic Properties of Determinants of Square Matrices over a Field

MATRIX12,

Xiquan Liang , Tao Sun and Dahai Hu. Some Properties of Line and Column Operations on Matrices

MATRIX13,

Karol P\c{a}k. Basic Properties of the Rank of Matrices over a Field

MATRIX14,

Yatsuka Nakamura , Kunio Oniumi and Wenpai Chang. Invertibility of Matrices of Field Elements

MATRIX15,

Karol P\c{a}k. Solutions of Linear Equations

MATRIX16,

Xiaopeng Yue and Xiquan Liang. Basic Properties of Circulant Matrices and Anti-circular Matrices

MATRIX_1,

Katarzyna Jankowska. Matrices. Abelian Group of Matrices

MATRIX_2,

Katarzyna Jankowska. Transpose Matrices and Groups of Permutations

MATRIX_3,

Katarzyna Zawadzka. The Product of Matrices of Elements of a Field and Determinants

MATRIX_4,

Yatsuka Nakamura and Hiroshi Yamazaki. Calculation of Matrices of Field Elements. Part {I}

MATRIX_5,

Wenpai Chang , Hiroshi Yamazaki and Yatsuka Nakamura. A Theory of Matrices of Complex Elements

MATRIX_6,

Xiaopeng Yue , Xiquan Liang and Zhongpin Sun. Some Properties Of Some Special Matrices

MATRIX_7,

Yatsuka Nakamura. Determinant of Some Matrices of Field Elements

MATRIX_8,

Xiaopeng Yue , Dahai Hu , Xiquan Liang and Zhongpin Sun. Some Properties Of Some Special Matrices, Part {II}

MATRIX_9,

Ewa Romanowicz and Adam Grabowski. On the Permanent of a Matrix

MATRIXC1,

Wenpai Chang , Hiroshi Yamazaki and Yatsuka Nakamura. The Inner Product and Conjugate of Matrix of Complex Numbers

MATRIXJ1,

Karol P\c{a}k. Block Diagonal Matrices

MATRIXJ2,

Karol P\c{a}k. Jordan Matrix Decomposition

MATRIXR1,

Yatsuka Nakamura , Nobuyuki Tamura and Wenpai Chang. A Theory of Matrices of Real Elements

MATRIXR2,

Nobuyuki Tamura and Yatsuka Nakamura. Determinant and Inverse of Matrices of Real Elements

MATRLIN,

Robert Milewski. Associated Matrix of Linear Map

MATRLIN2,

Karol P\c{a}k. Linear Map of Matrices

MATROID0,

Grzegorz Bancerek and Yasunari Shidama. Introduction to Matroids

MATRPROB,

Bo Zhang and Yatsuka Nakamura. The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements

MATRTOP1,

Karol P\kak. Linear Transformations of Euclidean Topological Spaces

MATRTOP2,

Karol P\kak. Linear Transformations of Euclidean Topological Spaces. Part {II}

MAZURULM,

Artur Korni{\l}owicz. Mazur-Ulam Theorem

MBOOLEAN,

Artur Korni{\l}owicz. Definitions and Basic Properties of Boolean & Union of Many Sorted Sets

MCART_1,

Andrzej Trybulec. Tuples, Projections and Cartesian Products

MCART_2,

Micha{\l} Muzalewski and Wojciech Skaba. N-Tuples and Cartesian Products for n=5

MEASURE1,

J\'ozef Bia{\l}as. The $\sigma$-additive Measure Theory

MEASURE2,

J\'ozef Bia{\l}as. Several Properties of the $\sigma$-additive Measure. Discrete categories

MEASURE3,

J\'ozef Bia{\l}as. Completeness of the $\sigma$-Additive Measure. Measure Theory

MEASURE4,

J\'ozef Bia{\l}as. Properties of Caratheodor's Measure

MEASURE5,

J\'ozef Bia{\l}as. Properties of the Intervals of Real Numbers

MEASURE6,

J\'ozef Bia\las. Some Properties of the Intervals

MEASURE7,

J\'ozef Bia{\l}as. The One-Dimensional Lebesgue Measure As an Example of a Formalization in the Mizar Language of the Classical Definition of a Mathematical Object

MEASURE8,

Noboru Endou , Hiroyuki Okazaki and Yasunari Shidama. The Hopf Extension Theorem of Measure

MEMBER_1,

Artur Korni{\l}owicz. Collective Operations on Number-Membered Sets

MEMBERED,

Andrzej Trybulec. On the Sets Inhabited by Numbers

MESFUN10,

Noboru Endou , Keiko Narita and Yasunari Shidama. Fatou's Lemma and the {L}ebesgue's Convergence Theorem

MESFUN6C,

Keiko Narita , Noboru Endou and Yasunari Shidama. Integral of Complex-Valued Measurable Function

MESFUN7C,

Keiko Narita , Noboru Endou and Yasunari Shidama. The Measurability of Complex-Valued Functional Sequences

MESFUN9C,

Keiko Narita , Noboru Endou and Yasunari Shidama. Lebesgue's Convergence Theorem of Complex-Valued Function

MESFUNC1,

Noboru Endou , Katsumi Wasaki and Yasunari Shidama. Definitions and Basic Properties of Measurable Functions

MESFUNC2,

Noboru Endou , Katsumi Wasaki and Yasunari Shidama. Measurability of Extended Real Valued Functions

MESFUNC3,

Yasunari Shidama and Noboru Endou. Lebesgue Integral of Simple Valued Function

MESFUNC4,

Noboru Endou and Yasunari Shidama. Linearity of {L}ebesgue Integral of Simple Valued Function

MESFUNC5,

Noboru Endou and Yasunari Shidama. Integral of Measurable Function

MESFUNC6,

Yasunari Shidama and Noboru Endou. Integral of Real-valued Measurable Function

MESFUNC7,

Keiko Narita , Noboru Endou and Yasunari Shidama. The First Mean Value Theorem for Integrals

MESFUNC8,

Noboru Endou , Yasunari Shidama and Keiko Narita. Egoroff's Theorem

MESFUNC9,

Noboru Endou , Keiko Narita and Yasunari Shidama. The Lebesgue Monotone Convergence Theorem

METRIC_1,

Stanis{\l}awa Kanas, Adam Lecko and Mariusz Startek. Metric Spaces

METRIC_2,

Adam Lecko and Mariusz Startek. On Pseudometric Spaces

METRIC_3,

Stanis{\l}awa Kanas and Jan Stankiewicz. Metrics in Cartesian Product

METRIC_6,

Stanis{\l}awa Kanas and Adam Lecko. Sequences in Metric Spaces

METRIZTS,

Karol P\c{a}k. Basic Properties of Metrizable Topological Spaces

MFOLD_1,

Marco Riccardi. The Definition of Topological Manifolds

MIDSP_1,

Micha{\l} Muzalewski. Midpoint algebras

MIDSP_2,

Micha{\l} Muzalewski. Atlas of Midpoint Algebra

MIDSP_3,

Micha{\l} Muzalewski. Reper Algebras

MOD_2,

Michal Muzalewski. Rings and Modules - Part II

MOD_3,

Michal Muzalewski. Free Modules

MOD_4,

Micha{\l} Muzalewski. Opposite Rings, Modules and their Morphisms

MODAL_1,

Alicia de la Cruz. Introduction to Modal Propositional Logic

MODCAT_1,

Micha{\l} Muzalewski. Category of Left Modules

MODELC_1,

Kazuhisa Ishida. Model Checking, Part {I}

MODELC_2,

Kazuhisa Ishida. Model Checking, Part II

MODELC_3,

Kazuhisa Ishida and Yasunari Shidama. Model Checking, Part {III}

MOEBIUS1,

Magdalena Jastrz\c{e}bska and Adam Grabowski. On the Properties of the {M}\"obius Function

MONOID_0,

Grzegorz Bancerek. Monoids

MONOID_1,

Grzegorz Bancerek. Monoid of Multisets and Subsets

MSAFREE,

Beata Perkowska. Free Many Sorted Universal Algebra

MSAFREE1,

Andrzej Trybulec. A Scheme for Extensions of Homomorphisms of Manysorted Algebras

MSAFREE2,

Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec and Pauline N. Kawamoto. Preliminaries to Circuits, II

MSAFREE3,

Grzegorz Bancerek and Artur Korni{\l}owicz. Yet another construction of free algebra

MSALIMIT,

Adam Grabowski. Inverse Limits of Many Sorted Algebras

MSATERM,

Grzegorz Bancerek. Terms over many sorted universal algebra

MSINST_1,

Adam Grabowski. Examples of Category Structures

MSSCYC_1,

Czes{\l}aw Byli\'nski and Piotr Rudnicki. The Correspondence Between Monotonic Many Sorted Signatures and Well-Founded Graphs. {P}art {I}

MSSCYC_2,

Czes{\l}aw Byli\'nski and Piotr Rudnicki. The Correspondence Between Monotonic Many Sorted Signatures and Well-Founded Graphs. {P}art {II}

MSSUBFAM,

Artur Korni{\l}owicz. Certain Facts about Families of Subsets of Many Sorted Sets

MSSUBLAT,

Adam Naumowicz and Agnieszka Julia Marasik. The Correspondence Between Lattices of Subalgebras of Universal Algebras and Many Sorted Algebras

MSUALG_1,

Andrzej Trybulec. Many Sorted Algebras

MSUALG_2,

Ewa Burakowska. Subalgebras of a Many Sorted Algebra. Lattice of Subalgebras

MSUALG_3,

Ma{\l}gorzata Korolkiewicz. Homomorphisms of Many Sorted Algebras

MSUALG_4,

Ma{\l}gorzata Korolkiewicz. Many Sorted Quotient Algebra

MSUALG_5,

Robert Milewski. Lattice of Congruences in a Many Sorted Algebra

MSUALG_6,

Grzegorz Bancerek. Translations, Endomorphisms, and Stable Equational Theories

MSUALG_7,

Robert Milewski. More on the Lattice of Many Sorted Equivalence Relations

MSUALG_8,

Robert Milewski. More on the Lattice of Congruences in a Many Sorted Algebra

MSUALG_9,

Artur Korni\l owicz. On the Trivial Many Sorted Algebras and Many Sorted Congruences

MSUHOM_1,

Adam Grabowski. The Correspondence Between Homomorphisms of Universal Algebra & Many Sorted Algebra

MULTOP_1,

Michal Muzalewski and Wojciech Skaba. Three-Argument Operations and Four-Argument Operations

MYCIELSK,

Piotr Rudnicki and Lorna Stewart. The {M}ycielskian of a Graph

N

NAGATA_1,

Karol P\c{a}k. The {N}agata-Smirnov Theorem. {P}art {I}

NAGATA_2,

Karol P\c{a}k. The {N}agata-Smirnov Theorem. {P}art {II}

NAT_1,

Grzegorz Bancerek. The Fundamental Properties of Natural Numbers

NAT_2,

Robert Milewski. Natural Numbers

NAT_3,

Artur Korni{\l}owicz and Piotr Rudnicki. Fundamental {T}heorem of {A}rithmetic

NAT_4,

Marco Riccardi. Pocklington's Theorem and {B}ertrand's Postulate

NAT_5,

Marco Riccardi. The Perfect Number Theorem and Wilson's Theorem

NAT_D,

Grzegorz Bancerek. Divisibility of Natural Numbers

NAT_LAT,

Marek Chmur. The Lattice of Natural Numbers and The Sublattice of it. The Set of Prime Numbers

NATTRA_1,

Andrzej Trybulec. Natural Transformations. Discrete Categories

NCFCONT1,

Noboru Endou. Continuous Functions on Real and Complex Normed Linear Spaces

NCFCONT2,

Noboru Endou. Uniform Continuity of Functions on Normed Complex Linear Spaces

NDIFF_1,

Hiroshi Imura , Morishige Kimura and Yasunari Shidama. The Differentiable Functions on Normed Linear Spaces

NDIFF_2,

Hiroshi Imura , Yuji Sakai and Yasunari Shidama. Differentiable Functions on Normed Linear Spaces. {P}art {II}

NDIFF_3,

Hiroyuki Okazaki , Noboru Endou , Keiko Narita and Yasunari Shidama. Differentiable Functions into Real Normed Spaces

NECKLA_2,

Krzysztof Retel. The Class of Series-Parallel Graphs, {II}

NECKLA_3,

Krzysztof Retel. The Class of Series-Parallel Graphs, {III}

NECKLACE,

Krzysztof Retel. The Class of Series-Parallel Graphs, {I}

NET_1,

Waldemar Korczy\'nski. Some Elementary Notions of the Theory of Petri Nets

NEWTON,

Rafa{\l} Kwiatek. Factorial and Newton coefficients

NFCONT_1,

Takaya Nishiyama, Keiji Ohkubo and Yasunari Shidama. The Continuous Functions on Normed Linear Spaces

NFCONT_2,

Takaya Nishiyama , Artur Korni{\l}owicz and Yasunari Shidama. The Uniform Continuity of Functions on Normed Linear Spaces

NFCONT_3,

Hiroyuki Okazaki , Noboru Endou and Yasunari Shidama. More on Continuous Functions on Normed Linear Spaces

NFCONT_4,

Keiko Narita , Artur Kornilowicz and Yasunari Shidama. More on the Continuity of Real Functions

NORMFORM,

Andrzej Trybulec. Algebra of Normal Forms

NORMSP_0,

Andrzej Trybulec. Preliminaries to Normed Spaces

NORMSP_1,

Jan Popio{\l}ek. Real Normed Space

NORMSP_2,

Noboru Endou , Yasunari Shidama and Katsumasa Okamura. Baire's Category Theorem and Some Spaces Generated from Real Normed Space

NUMBERS,

Andrzej Trybulec. Subsets of Complex Numbers

NUMERAL1,

Adam Naumowicz. On the Representation of Natural Numbers in Positional Numeral Systems

NUMERALS,

Library Committee. Numerals - Requirements

O

O_RING_1,

Micha{\l} Muzalewski and Les{\l}aw W. Szczerba. Ordered Rings - Part I

OPENLATT,

Jolanta Kamie\'nska. Representation Theorem for Heyting Lattices

OPOSET_1,

Markus Moschner. Basic Notions and Properties of Orthoposets

OPPCAT_1,

Czes\l aw Byli\'nski. Opposite Categories and Contravariant Functors

ORDERS_1,

Wojciech A. Trybulec. Partially Ordered Sets

ORDERS_2,

Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn Lemma

ORDERS_3,

Adam Grabowski. On the Category of Posets

ORDERS_4,

Marta Pruszy\'nska and Marek Dudzicz. On the Isomorphism Between Finite Chains

ORDINAL1,

Grzegorz Bancerek. The Ordinal Numbers. Transfinite Induction and Defining by Transfinite Induction

ORDINAL2,

Grzegorz Bancerek. Sequences of Ordinal Numbers. Beginnings of Ordinal Arithmetics

ORDINAL3,

Grzegorz Bancerek. Ordinal Arithmetics

ORDINAL4,

Grzegorz Bancerek. Increasing and Continuous Ordinal Sequences

ORDINAL5,

Grzegorz Bancerek. Epsilon Numbers and Cantor Normal Form

ORDINAL6,

Grzegorz Bancerek. Veblen Hierarchy

ORTSP_1,

Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski. Construction of a bilinear symmetric form in orthogonal vector space

OSAFREE,

Josef Urban. Free Order Sorted Universal Algebra

OSALG_1,

Josef Urban. Order Sorted Algebras

OSALG_2,

Josef Urban. Subalgebras of a Order Sorted Algebra. {L}attice of Subalgebras

OSALG_3,

Josef Urban. Homomorphisms of Order Sorted Algebras

OSALG_4,

Josef Urban. Order Sorted Quotient Algebra

P

PAPDESAF,

Krzysztof Pra\.zmowski. Fanoian, Pappian and Desarguesian Affine Spaces

PARDEPAP,

Krzysztof Pra\.zmowski and Krzysztof Radziszewski. Elementary Variants of Affine Configurational Theorems

PARSP_1,

Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski. Parallelity Spaces

PARSP_2,

Eugeniusz Kusak and Wojciech Leo\'nczuk. Fano-Desargues Parallelity Spaces

PARTFUN1,

Czes{\l}aw Byli\'nski. Partial Functions

PARTFUN2,

Jaros{\l}aw Kotowicz. Partial Functions from a Domain to a Domain

PARTFUN3,

Artur Korni{\l}owicz. On the Real Valued Functions

PARTIT1,

Shunichi Kobayashi and Kui Jia. A theory of partitions, { I }

PARTIT_2,

Andrzej Trybulec. Classes of Independent Partitions

PASCH,

Henryk Oryszczyszyn, Krzysztof Pra\.zmowski and. Classical and Non--classical Pasch Configurations in Ordered Affine Planes

PBOOLE,

Andrzej Trybulec. Manysorted Sets

PCOMPS_1,

Leszek Borys. Paracompact and Metrizable Spaces

PCOMPS_2,

Leszek Borys. On Paracompactness of Metrizable Spaces

PCS_0,

Klaus E. Grue and Artur Korni{\l}owicz. Basic Operations on Preordered Coherent Spaces

PDIFF_1,

Noboru Endou , Yasunari Shidama and Keiichi Miyajima. Partial Differentiation on Normed Linear Spaces $ {\cal R}^n$

PDIFF_2,

Bing Xie , Xiquan Liang , Hongwei Li and Yanping Zhuang. Partial Differentiation of Real Binary Functions

PDIFF_3,

Bing Xie , Xiquan Liang and Xiuzhuan Shen. Second-order Partial Differentiation of Real Binary Functions

PDIFF_4,

Takao Inou\'e , Bing Xie and Xiquan Liang. Partial Differentiation of Real Ternary Functions

PDIFF_5,

Takao Inou\'e. Second-order Partial Differentiation of Real Ternary Functions

PDIFF_6,

Takao Inou\'e , Noboru Endou and Yasunari Shidama. Differentiation of Vector-Valued Functions on $n$-Dimensional Real Normed Linear Spaces

PDIFF_7,

Takao Inou\'e , Adam Naumowicz , Noboru Endou and Yasunari Shidama. Partial Differentiation of Vector-Valued Functions on $n$-Dimensional Real Normed Linear Spaces

PDIFF_8,

Takao Inou\'e , Adam Naumowicz , Noboru Endou and Yasunari Shidama. Partial Differentiation, Differentiation and Continuity on $n$-Dimensional Real Normed Linear Spaces

PENCIL_1,

Adam Naumowicz. On Segre's Product of Partial Line Spaces

PENCIL_2,

Adam Naumowicz. On Cosets in Segre's Product of Partial Linear Spaces

PENCIL_3,

Adam Naumowicz. On the Characterization of Collineations of the Segre Product of Strongly Connected Partial Linear Spaces

PENCIL_4,

Adam Naumowicz. Spaces of Pencils, {G}rassmann Spaces, and Generalized {V}eronese Spaces

PEPIN,

Yoshinori Fujisawa , Yasushi Fuwa and Hidetaka Shimizu. Public-Key Cryptography and Pepin's Test for the Primality of Fermat Numbers

PETRI,

Pauline N. Kawamoto, Yasushi Fuwa and Yatsuka Nakamura. Basic Petri Net Concepts. Place/Transition Net Structure, Deadlocks, Traps, Dual Nets

PETRI_2,

Mitsuru Jitsukawa, Pauline N. Kawamoto, Yasunari Shidama,. Cell Petri Net Concepts

PNPROC_1,

Grzegorz Bancerek , Mitsuru Aoki , Akio Matsumoto and Yasunari Shidama. Processes in {P}etri nets

POLYALG1,

Ewa Gr\c{a}dzka. The Algebra of Polynomials

POLYEQ_1,

Liang Xiquan. Solving Roots of Polynomial Equations of Degree 2 and 3 with Real Coefficients

POLYEQ_2,

Xiquan Liang. Solving Roots of Polynomial Equation of Degree 4 with Real Coefficients

POLYEQ_3,

Yuzhong Ding and Xiquan Liang. Solving Complex Roots of Polynomial Equation of Degree 2 and 3 with Complex Coefficients

POLYEQ_4,

Yuzhong Ding and Xiquan Liang. Solving the Roots of the Special Polynomial Equation with Real Coefficients

POLYEQ_5,

Marco Riccardi. Solution of Cubic and Quartic Equations

POLYFORM,

Jesse Alama. Euler's Polyhedron Formula

POLYNOM1,

Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables

POLYNOM2,

Christoph Schwarzweller and Andrzej Trybulec. Evaluation of Multivariate Polynomials

POLYNOM3,

Robert Milewski. The Ring of Polynomials

POLYNOM4,

Robert Milewski. Evaluation of Polynomials

POLYNOM5,

Robert Milewski. Fundamental Theorem of Algebra

POLYNOM6,

Barbara Dzienis. On polynomials with coefficients in a ring of polynomials

POLYNOM7,

Christoph Schwarzweller. More About Polynomials: Monomials and Constant Polynomials

POLYNOM8,

Krzysztof Treyderowski and Christoph Schwarzweller. Multiplication of Polynomials using {D}iscrete {F}ourier {T}ransformation

POLYRED,

Christoph Schwarzweller. Polynomial Reduction

POSET_1,

Kazuhisa Ishida and Yasunari Shidama. Fix-point Theorem for Continuous Functions on Chain-complete Posets

POWER,

Konrad Raczkowski and Andrzej N\c{e}dzusiak. Real Exponents and Logarithms

PRALG_1,

Beata Madras. Product of Family of Universal Algebras

PRALG_2,

Beata Madras. Products of Many Sorted Algebras

PRALG_3,

Mariusz Giero. More on Products of Many Sorted Algebras

PRE_CIRC,

Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec and Pauline N. Kawamoto. Preliminaries to Circuits, I

PRE_FF,

Grzegorz Bancerek and Piotr Rudnicki. Two Programs for {\bf SCM}. Part I - Preliminaries

PRE_POLY,

Andrzej Trybulec. Preliminaries to Polynomials

PRE_TOPC,

Beata Padlewska and Agata Darmochwa\l. Topological Spaces and Continuous Functions

PRELAMB,

Wojciech Zielonka. Preliminaries to the Lambek Calculus

PREPOWER,

Konrad Raczkowski. Integer and Rational Exponents

PRGCOR_1,

Yatsuka Nakamura. Correctness of Non Overwriting Programs. {P}art {I}

PRGCOR_2,

Takaya Nishiyama , Hirofumi Fukura and Yatsuka Nakamura. Logical Correctness of Vector Calculation Programs

PROB_1,

Andrzej N\c{e}dzusiak. $\sigma$-Fields and Probability

PROB_2,

Andrzej N\c{e}dzusiak. Probability. Independence of Events and Conditional Probability

PROB_3,

Bo Zhang , Hiroshi Yamazaki and Yatsuka Nakamura. Set Sequences and Monotone Class

PROB_4,

Bo Zhang , Hiroshi Yamazaki and Yatsuka Nakamura. The Relevance of Measure and Probability and Definition of Completeness of Probability

PROCAL_1,

Jan Popio{\l}ek and Andrzej Trybulec. Calculus of Propositions

PROJDES1,

Eugeniusz Kusak. Desargues Theorem In Projective 3-Space

PROJPL_1,

Micha{\l} Muzalewski. Projective {P}lanes

PROJRED1,

Eugeniusz Kusak and Wojciech Leo\'nczuk. Incidence Projective Space (a reduction theorem in a plane)

PROJRED2,

Eugeniusz Kusak, Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski. On Projections in Projective Planes. Part II

PRVECT_1,

Anna Lango and Grzegorz Bancerek. Product of Families of Groups and Vector Spaces

PRVECT_2,

Noboru Endou , Yasunari Shidama and Keiichi Miyajima. The Product Space of Real Normed Spaces and Its Properties

PRVECT_3,

Hiroyuki Okazaki , Noboru Endou and Yasunari Shidama. Cartesian Products of Family of Real Linear Spaces

PSCOMP_1,

Czes{\l}aw Byli\'nski and Piotr Rudnicki. Bounding boxes for compact sets in ${\calE}^2$

PUA2MSS1,

Grzegorz Bancerek. Minimal Manysorted Signature for Partial Algebra

PYTHTRIP,

Freek Wiedijk. Pythagorean triples

PZFMISC1,

Artur Korni{\l}owicz. Some Basic Properties of Many Sorted Sets

Q

QC_LANG1,

Piotr Rudnicki and Andrzej Trybulec. A First Order Language

QC_LANG2,

Grzegorz Bancerek. Connectives and Subformulae of the First Order Language

QC_LANG3,

Czes{\l}aw Byli\'nski and Grzegorz Bancerek. Variables in Formulae of the First Order Language

QC_LANG4,

Oleg Okhotnikov. The Subformula Tree of a Formula of the First Order Language

QMAX_1,

Pawe{\l} Sadowski, Andrzej Trybulec and Konrad Raczkowski. The Fundamental Logic Structure in Quantum Mechanics

QUANTAL1,

Grzegorz Bancerek. Quantales

QUATERN2,

Fuguo Ge. Inner Products, Group, Ring of Quaternion Numbers

QUATERN3,

Bo Li , Pan Wang , Xiquan Liang and Yanping Zhuang. Some Operations on Quaternion Numbers

QUATERNI,

Xiquan Liang and Fuguo Ge. The Quaternion Numbers

QUIN_1,

Jan Popio\l ek. Quadratic Inequalities

QUOFIELD,

Christoph Schwarzweller. The Field of Quotients over an Integral Domain

R

RADIX_1,

Yoshinori Fujisawa and Yasushi Fuwa. Definitions of Radix-2k Signed-Digit number and its adder algorithm

RADIX_2,

Yasushi Fuwa and Yoshinori Fujisawa. High-speed algorithms for RSA cryptograms

RADIX_3,

Masaaki Niimura and Yasushi Fuwa. Improvement of Radix-$2^k$ Signed-Digit Number for High Speed Circuit

RADIX_4,

Masaaki Niimura and Yasushi Fuwa. High Speed Adder Algorithm with Radix-$2^k$ SD_Sub Number

RADIX_5,

Masaaki Niimura and Yasushi Fuwa. Magnitude Relation Properties of Radix-$2^k$ SD Number

RADIX_6,

Masaaki Niimura and Yasushi Fuwa. High Speed Modulo Calculation Algorithm with Radix-$2^k$ SD Number

RAMSEY_1,

Marco Riccardi. Ramsey's Theorem

RANDOM_1,

Hiroyuki Okazaki and Yasunari Shidama. Probability on Finite Set and Real Valued Random Variables

RANDOM_2,

Hiroyuki Okazaki and Yasunari Shidama. Probability Measure on Discrete Spaces and Algebra of Real Valued Random Variables

RANKNULL,

Jesse Alama. The Rank+Nullity Theorem

RAT_1,

Andrzej Kondracki. Basic Properties of Rational Numbers

RCOMP_1,

Konrad Raczkowski and Pawe{\l} Sadowski. Topological Properties of Subsets in Real Numbers

RCOMP_3,

Artur Korni{\l}owicz. Properties of Connected Subsets of the Real Line

REAL,

Library Committee. Basic Properties of Real Numbers - Requirements

REAL_1,

Krzysztof Hryniewiecki. Basic Properties of Real Numbers

REAL_3,

Bo Li , Yan Zhang and Artur Korni{\l}owicz. Simple Continued Fractions and Their Convergents

REAL_LAT,

Marek Chmur. The Lattice of Real Numbers. The Lattice of Real Functions

REAL_NS1,

Noboru Endou and Yasunari Shidama. Completeness of the Real {E}uclidean Space

REALSET1,

J\'ozef Bia{\l}as. Group and Field Definitions

REALSET2,

J\'ozef Bia{\l}as. Properties of Fields

REALSET3,

J\'ozef Bia{\l}as. Several Properties of Fields. Field Theory

REARRAN1,

Yuji Sakai and Jaros{\l}aw Kotowicz. Introduction to Theory of Rearrangment

RECDEF_1,

Krzysztof Hryniewiecki. Recursive Definitions

RECDEF_2,

Artur Korni{\l}owicz. Recursive Definitions. {P}art {II}

RELAT_1,

Edmund Woronowicz. Relations and Their Basic Properties

RELAT_2,

Edmund Woronowicz and Anna Zalewska. Properties of Binary Relations

RELOC,

Yasushi Tanaka. Relocatability

RELSET_1,

Edmund Woronowicz. Relations Defined on Sets

RELSET_2,

Krzysztof Retel. Properties of First and Second Order Cutting of Binary Relations

REVROT_1,

Andrzej Trybulec. Rotating and reversing.(Finite sequences)

REWRITE1,

Grzegorz Bancerek. Reduction Relations

REWRITE2,

Micha{\l} Trybulec. String Rewriting Systems

REWRITE3,

Micha{\l} Trybulec. Labelled State Transition Systems

RFINSEQ,

Jaros{\l}aw Kotowicz. Functions and Finite Sequences of Real Numbers

RFINSEQ2,

Yatsuka Nakamura. Sorting Operators for Finite Sequences

RFUNCT_1,

Jaros{\l}aw Kotowicz. Partial Functions from a Domain to the Set of Real Numbers

RFUNCT_2,

Jaros{\l}aw Kotowicz. Properties of Real Functions

RFUNCT_3,

Jaros{\l}aw Kotowicz and Yuji Sakai. Properties of Partial Functions from a Domain to the Set of Real Numbers

RFUNCT_4,

Noboru Endou , Katsumi Wasaki and Yasunari Shidama. Introduction to Several Concepts of Convexity and Semicontinuity for Function from REAL to REAL

RINFSUP1,

Bo Zhang , Hiroshi Yamazaki and Yatsuka Nakamura. Inferior Limit and Superior Limit of Sequences of Real Numbers

RINFSUP2,

Hiroshi Yamazaki , Noboru Endou , Yasunari Shidama and Hiroyuki Okazaki. Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers

RING_1,

Artur Korni{\l}owicz. Quotient Rings

RINGCAT1,

Micha{\l} Muzalewski. Category of Rings

RLAFFIN1,

Karol P\c{a}k. Affine Independence in Vector Spaces

RLAFFIN2,

Karol P\c{a}k. The Geometric Interior in Real Linear Spaces

RLAFFIN3,

Karol P\kak. Continuity of Barycentric Coordinates in Euclidean Topological Spaces

RLSUB_1,

Wojciech A. Trybulec. Subspaces and Cosets of Subspaces in Real Linear Space

RLSUB_2,

Wojciech A. Trybulec. Operations on Subspaces in Real Linear Space

RLTOPSP1,

Czes{\l}aw Byli\'nski. Introduction to Real Linear Topological Spaces

RLVECT_1,

Wojciech A. Trybulec. Vectors in Real Linear Space

RLVECT_2,

Wojciech A. Trybulec. Linear Combinations in Real Linear Space

RLVECT_3,

Wojciech A. Trybulec. Basis of Real Linear Space

RLVECT_4,

Wojciech A. Trybulec. Subspaces of Real Linear Space Generated by One, Two, or Three Vectors and Their Cosets

RLVECT_5,

JingChao Chen. The Steinitz Theorem and the Dimension of a Real Linear Space

RLVECT_X,

Yuichi Futa , Hiroyuki Okazaki and Yasunari Shidama. Formalization of Integral Linear Space

RMOD_2,

Michal Muzalewski and Wojciech Skaba. Submodules and Cosets of Submodules in Right Module over Associative Ring

RMOD_3,

Michal Muzalewski and Wojciech Skaba. Operations on Submodules in Right Module over Associative Ring

RMOD_4,

Michal Muzalewski and Wojciech Skaba. Linear Combinations in Right Module over Associative Ring

ROBBINS1,

Adam Grabowski. Robbins Algebras vs. Boolean Algebras

ROBBINS2,

Wioletta Truszkowska and Adam Grabowski. On the Two Short Axiomatizations of Ortholattices

ROBBINS3,

Adam Grabowski and Markus Moschner. Formalization of Ortholattices via Orthoposets

ROBBINS4,

El\.zbieta M\c{a}dra and Adam Grabowski. Orthomodular Lattices

ROLLE,

Jaros{\l}aw Kotowicz, Konrad Raczkowski and Pawe{\l} Sadowski. Average Value Theorems for Real Functions of One Variable

ROUGHS_1,

Adam Grabowski. Basic Properties of Rough Sets and Rough Membership Function

RPR_1,

Jan Popio{\l}ek. Introduction to Probability

RSSPACE,

Noboru Endou , Yasumasa Suzuki and Yasunari Shidama. Real Linear Space of Real Sequences

RSSPACE2,

Noboru Endou , Yasumasa Suzuki and Yasunari Shidama. Hilbert Space of Real Sequences

RSSPACE3,

Yasumasa Suzuki, Noboru Endou and Yasunari Shidama. Banach Space of Absolute Summable Real Sequences

RSSPACE4,

Yasumasa Suzuki. Banach Space of Bounded Real Sequences

RUSUB_1,

Noboru Endou , Takashi Mitsuishi and Yasunari Shidama. Subspaces and Cosets of Subspace of Real Unitary Space

RUSUB_2,

Noboru Endou , Takashi Mitsuishi and Yasunari Shidama. Operations on Subspaces in Real Unitary Space

RUSUB_3,

Noboru Endou , Takashi Mitsuishi and Yasunari Shidama. Linear Combinations in Real Unitary Space

RUSUB_4,

Noboru Endou , Takashi Mitsuishi and Yasunari Shidama. Dimension of Real Unitary Space

RUSUB_5,

Noboru Endou , Takashi Mitsuishi and Yasunari Shidama. Topology of Real Unitary Space

RVSUM_1,

Czes{\l}aw Byli\'nski. The Sum and Product of Finite Sequences of Real Numbers

RVSUM_2,

Keiichi Miyajima and Takahiro Kato. The Sum and Product of Finite Sequences of Complex Numbers

S

SCHEME1,

Jaros{\l}aw Kotowicz. Schemes of Existence of some Types of Functions

SCHEMS_1,

Stanis\l aw T. Czuba. Schemes

SCM_1,

Grzegorz Bancerek and Piotr Rudnicki. Development of Terminology for {\bf SCM}

SCM_COMP,

Grzegorz Bancerek and Piotr Rudnicki. A compiler of arithmetic expressions for { \bf SCM }

SCM_HALT,

JingChao Chen and Yatsuka Nakamura. Initialization Halting Concepts and Their Basic Properties of SCM+FSA

SCMBSORT,

JingChao Chen and Yatsuka Nakamura. Bubble Sort on SCM+FSA

SCMFSA10,

Artur Korni{\l}owicz. On the Instructions of { \bf SCM+FSA }

SCMFSA6A,

Andrzej Trybulec , Yatsuka Nakamura and Noriko Asamoto. On the compositions of macro instructions

SCMFSA6B,

Noriko Asamoto , Yatsuka Nakamura , Piotr Rudnicki and Andrzej Trybulec. On the compositions of macro instructions, Part II

SCMFSA6C,

Noriko Asamoto , Yatsuka Nakamura , Piotr Rudnicki and Andrzej Trybulec. On the compositions of macro instructions, Part III

SCMFSA7B,

Noriko Asamoto. Constant assignment macro instructions of SCM+FSA, Part II

SCMFSA8A,

Noriko Asamoto. Conditional branch macro instructions of SCM+FSA, Part I (preliminary)

SCMFSA8B,

Noriko Asamoto. Conditional branch macro instructions of SCM+FSA, Part II

SCMFSA8C,

Noriko Asamoto. The {\bf loop} and {\bf Times} Macroinstruction for {\SCMFSA}

SCMFSA9A,

Piotr Rudnicki. The { \bf while } macro instructions of SCM+FSA, Part { II }

SCMFSA_1,

Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki. An Extension of { \bf SCM }

SCMFSA_2,

Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki. The { \bf SCM_FSA } computer

SCMFSA_3,

Andrzej Trybulec and Yatsuka Nakamura. Computation in { \bf SCM_FSA }

SCMFSA_4,

Andrzej Trybulec and Yatsuka Nakamura. Modifying addresses of instructions of { \bf SCM_FSA }

SCMFSA_5,

Andrzej Trybulec and Yatsuka Nakamura. Relocability for { \bf SCM_FSA }

SCMFSA_7,

Noriko Asamoto. Some Multi-instructions defined by sequence of instructions of SCM+FSA

SCMFSA_9,

Jing-Chao Chen. While Macro Instructions of SCM+FSA

SCMISORT,

JingChao Chen. Insert Sort on SCM+FSA

SCMP_GCD,

JingChao Chen. Recursive Euclide Algorithm

SCMPDS_1,

JingChao Chen. A Small Computer Model with Push-Down Stack

SCMPDS_2,

JingChao Chen. The SCMPDS Computer and the Basic Semantics of Its Instructions

SCMPDS_3,

JingChao Chen. Computation and Program Shift in the SCMPDS Computer

SCMPDS_4,

JingChao Chen. The Construction and shiftability of Program Blocks for SCMPDS

SCMPDS_5,

JingChao Chen. Computation of Two Consecutive Program Blocks for SCMPDS

SCMPDS_6,

JingChao Chen. The Construction and Computation of Conditional Statements for SCMPDS

SCMPDS_7,

JingChao Chen and Piotr Rudnicki. The Construction and Computation of For-loop Programs for SCMPDS

SCMPDS_8,

JingChao Chen. The Construction and Computation of While-loop Programs for SCMPDS

SCMPDS_9,

Artur Korni{\l}owicz and Yasunari Shidama. SCMPDS Is Not Standard

SCMRING1,

Artur Korni{\l}owicz. The Construction of { \bf SCM } over Ring

SCMRING2,

Artur Korni{\l}owicz. The Basic Properties of { \bf SCM } over Ring

SCMRING3,

Artur Korni{\l}owicz. The Properties of Instructions of { \bf SCM } over Ring

SCMRING4,

Artur Korni{\l}owicz and Yasunari Shidama. Relocability for { \bf SCM } over Ring

SCPINVAR,

JingChao Chen. Justifying the Correctness of Fibonacci Sequence and Euclide Algorithm by Loop Invariant

SCPISORT,

JingChao Chen. Insert Sort on SCMPDS

SCPQSORT,

JingChao Chen. Quick Sort on SCMPDS

SEMI_AF1,

Eugeniusz Kusak and Krzysztof Radziszewski. Semi-Affine Space

SEQ_1,

Jaros{\l}aw Kotowicz. Real Sequences and Basic Operations on Them

SEQ_2,

Jaros{\l}aw Kotowicz. Convergent Sequences and the Limit of Sequences

SEQ_4,

Jaros{\l}aw Kotowicz. Convergent Real Sequences. Upper and Lower Bound of Sets of Real Numbers

SEQFUNC,

Beata Perkowska. Functional Sequence from a Domain to a Domain

SEQM_3,

Jaros{\l}aw Kotowicz. Monotone Real Sequences. Subsequences

SERIES_1,

Konrad Raczkowski and Andrzej N\c{e}dzusiak. Series

SERIES_2,

Ming Liang and Yuzhong Ding. Partial Sum of Some Series

SERIES_3,

Fuguo Ge and Xiquan Liang. On the Partial Product of Series and Related Basic Inequalities

SERIES_4,

Jianbing Cao , Fahui Zhai and Xiquan Liang. Partial Sum and Partial Product of Some Series

SERIES_5,

Fuguo Ge and Xiquan Liang. On the Partial Product and Partial Sum of Series and Related Basic Inequalities

SETFAM_1,

Beata Padlewska. Families of Sets

SETLIM_1,

Bo Zhang , Hiroshi Yamazaki and Yatsuka Nakamura. Limit of Sequence of Subsets

SETLIM_2,

Bo Zhang , Hiroshi Yamazaki and Yatsuka Nakamura. Some Equations Related to the Limit of Sequence of Subsets

SETWISEO,

Andrzej Trybulec. Semilattice Operations on Finite Subsets

SETWOP_2,

Czes{\l}aw Byli\'nski. Semigroup operations on finite subsets

SF_MASTR,

Piotr Rudnicki and Andrzej Trybulec. Memory handling for SCM+FSA

SFMASTR1,

Piotr Rudnicki. On the Composition of non-parahalting Macro Instructions

SFMASTR2,

Piotr Rudnicki. Another { \bf times } Macro Instruction

SFMASTR3,

Piotr Rudnicki. The { \bf for } (going up) Macro Instruction

SGRAPH1,

Yozo Toda. The Formalisation of Simple Graphs

SHEFFER1,

Violetta Kozarkiewicz and Adam Grabowski. Axiomatization of {B}oolean Algebras Based on Sheffer Stroke

SHEFFER2,

Aneta {\L}ukaszuk and Adam Grabowski. Short {S}heffer Stroke-Based Single Axiom for {B}oolean Algebras

SIMPLEX0,

Karol P\c{a}k. Abstract Simplicial Complexes

SIMPLEX1,

Karol P\c{a}k. Sperner's Lemma

SIMPLEX2,

Karol P\kak. Brouwer Fixed Point Theorem for Simplexes

SIN_COS,

Yuguang Yang and Yasunari Shidama. Trigonometric Functions and Existence of Circle Ratio

SIN_COS2,

Takashi Mitsuishi and Yuguang Yang. Properties of Trigonometric Function

SIN_COS3,

Takashi Mitsuishi , Noboru Endou and Keiji Ohkubo. Trigonometric Functions on Complex Space

SIN_COS4,

Pacharapokin Chanapat, Kanchun and Hiroshi Yamazaki. Formulas And Identities of Trigonometric Functions

SIN_COS5,

Yuzhong Ding and Xiquan Liang. Formulas And Identities of Trigonometric Functions

SIN_COS6,

Artur Korni{\l}owicz and Yasunari Shidama. Inverse Trigonometric Functions Arcsin and Arccos

SIN_COS7,

Fuguo Ge , Xiquan Liang and Yuzhong Ding. Formulas And Identities of Inverse Hyperbolic Functions

SIN_COS8,

Pacharapokin Chanapat and Hiroshi Yamazaki. Formulas and Identities of Hyperbolic Functions

SIN_COS9,

Xiquan Liang and Bing Xie. Inverse Trigonometric Functions Arctan and Arccot

SINCOS10,

Bing Xie , Xiquan Liang and Fuguo Ge. Inverse Trigonometric Functions Arcsec1, Arcsec2, Arccosec1 and Arccosec2

SPPOL_1,

Yatsuka Nakamura and Czes\law Byli\'nski. Extremal Properties of Vertices on Special Polygons I

SPPOL_2,

Czes\law Byli\'nski and Yatsuka Nakamura. Special Polygons

SPRECT_1,

Andrzej Trybulec and Yatsuka Nakamura. On Rectangular Finite Sequences of the Points of the Plane

SPRECT_2,

Andrzej Trybulec and Yatsuka Nakamura. On the Order on a Special Polygon

SPRECT_3,

Andrzej Trybulec and Yatsuka Nakamura. Some properties of special polygonal curves

SPRECT_4,

Andrzej Trybulec and Yatsuka Nakamura. On the components of the complement of a special polygonal curve

SPRECT_5,

Andrzej Trybulec and Yatsuka Nakamura. Again on the Order on a Special Polygon

SQUARE_1,

Andrzej Trybulec and Czes{\l}aw Byli\'nski. Some Properties of Real Numbers. Operations: min, max, square, and square root

STACKS_1,

Grzegorz Bancerek. Representation Theorem for Stacks

STIRL2_1,

Karol P\c{a}k. Stirling Numbers of the Second Kind

STRUCT_0,

Library Committee. Preliminaries to Structures

SUBLEMMA,

Patrick Braselmann and Peter Koepke. Coincidence Lemma and Substitution Lemma

SUBSET,

Library Committee. Basic Properties of Subsets - Requirements

SUBSET_1,

Zinaida Trybulec. Properties of Subsets

SUBSTLAT,

Adam Grabowski. Lattice of Substitutions

SUBSTUT1,

Patrick Braselmann and Peter Koepke. Substitution in First-Order Formulas: Elementary Properties

SUBSTUT2,

Patrick Braselmann and Peter Koepke. Substitution in First-Order Formulas -- Part II. {T}he Construction of First-Order Formulas

SUPINF_1,

J\'ozef Bia{\l}as. Infimum and Supremum of the Set of Real Numbers. Measure Theory

SUPINF_2,

J\'ozef Bia{\l}as. Series of Positive Real Numbers. Measure Theory

SYMSP_1,

Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski. Construction of a bilinear antisymmetric form in symplectic vector space

SYSREL,

Waldemar Korczy\'nski. Some Properties of Binary Relations

T

T_0TOPSP,

Mariusz \.Zynel and Adam Guzowski. $T_0$ Topological Spaces

T_1TOPSP,

Adam Naumowicz and Mariusz {\L}api\'nski. On $T_{1}$ Reflex of Topological Space

TARSKI,

Andrzej Trybulec. Tarski {G}rothendieck Set Theory

TAXONOM1,

Mariusz Giero and Roman Matuszewski. Lower Tolerance. {P}reliminaries to {W}roclaw Taxonomy

TAXONOM2,

Mariusz Giero. Hierarchies and Classifications of Sets

TAYLOR_1,

Yasunari Shidama. The {T}aylor Expansions

TAYLOR_2,

Akira Nishino and Yasunari Shidama. The {M}aclaurin Expansions

TBSP_1,

Alicia de la Cruz. Totally Bounded Metric Spaces

TDGROUP,

Grzegorz Lewandowski and Krzysztof Pra\.zmowski. A Construction of an Abstract Space of Congruence of Vectors

TDLAT_1,

Toshihiko Watanabe. The Lattice of Domains_of of a Topological Space

TDLAT_2,

Zbigniew Karno and Toshihiko Watanabe. Completeness of the Lattices of Domains of a Topological Space

TDLAT_3,

Zbigniew Karno. The Lattice of Domains of an Extremally Disconnected Space

TERMORD,

Christoph Schwarzweller. Term Orders

TEX_1,

Zbigniew Karno. On Discrete and Almost Discrete Topological Spaces

TEX_2,

Zbigniew Karno. Maximal Discrete Subspaces of Almost Discrete Topological Spaces

TEX_3,

Zbigniew Karno. On Nowhere and Everywhere Dense Subspaces of Topological Spaces

TEX_4,

Zbigniew Karno. Maximal Anti-Discrete Subspaces of Topological Spaces

TIETZE,

Artur Korni{\l}owicz , Grzegorz Bancerek and Adam Naumowicz. Tietze {E}xtension {T}heorem

TMAP_1,

Zbigniew Karno. Continuity of Mappings over the Union of Subspaces

TOLER_1,

Krzysztof Hryniewiecki. Relations of Tolerance

TOPALG_1,

Artur Korni{\l}owicz , Yasunari Shidama and Adam Grabowski. The Fundamental Group

TOPALG_2,

Artur Korni{\l}owicz. The Fundamental Group of Convex Subspaces of TOP-REAL n

TOPALG_3,

Artur Korni{\l}owicz. On the Isomorphism of Fundamental Groups

TOPALG_4,

Artur Korni{\l}owicz. On the Fundamental Groups of Products of Topological Spaces

TOPALG_5,

Artur Korni{\l}owicz. The Fundamental Group of the Circle

TOPDIM_1,

Karol P\c{a}k. Small {I}nductive {D}imension of {T}opological {S}paces

TOPDIM_2,

Karol P\c{a}k. Small Inductive Dimension of Topological Spaces, Part {II}

TOPGEN_1,

Adam Grabowski. On the Boundary and Derivative of a Set

TOPGEN_2,

Grzegorz Bancerek. On the characteristic and weight of a topological space

TOPGEN_3,

Grzegorz Bancerek. On constructing topological spaces and Sorgenfrey line

TOPGEN_4,

Adam Grabowski. On the {B}orel Families of Subsets of Topological Spaces

TOPGEN_5,

Grzegorz Bancerek. Niemytzki Plane -- an Example of {T}ychonoff Space Which Is Not $T_4$

TOPGRP_1,

Artur Korni{\l}owicz. The Definition and Basic Properties of Topological Groups

TOPMETR,

Agata Darmochwa{\l} and Yatsuka Nakamura. Metric Spaces as Topological Spaces - Fundamental Concepts

TOPMETR2,

Yatsuka Nakamura and Agata Darmochwa{\l}. Some Facts about Union of Two Functions and Continuity of Union of Functions

TOPMETR3,

Yatsuka Nakamura and Andrzej Trybulec. Sequences of Metric Spaces and an Abstract Intermediate Value Theorem

TOPREAL1,

Agata Darmochwa{\l} and Yatsuka Nakamura. The Topological Space ${\calE}^2_{\rm T}$. Arcs, Line Segments and Special Polygonal Arcs

TOPREAL2,

Agata Darmochwa{\l} and Yatsuka Nakamura. The Topological Space ${\calE}^2_{\rm T}$. Simple Closed Curves

TOPREAL3,

Yatsuka Nakamura and Jaros{\l}aw Kotowicz. Basic Properties of Connecting Points with Line Segments in ${\calE}^2_{\rm T}$

TOPREAL4,

Yatsuka Nakamura and Jaros{\l}aw Kotowicz. Connectedness Conditions Using Polygonal Arcs

TOPREAL5,

Yatsuka Nakamura and Andrzej Trybulec. Intermediate Value Theorem and Thickness of Simple Closed Curves

TOPREAL6,

Artur Korni{\l}owicz. Compactness of the Bounded Closed Subsets of TOP-REAL 2

TOPREAL7,

Artur Korni{\l}owicz. Homeomorphism between [:TOP-REAL i,TOP-REAL j:] and TOP-REAL (i+j)

TOPREAL8,

Andrzej Trybulec. More on the Finite Sequences on the Plane

TOPREAL9,

Artur Korni{\l}owicz and Yasunari Shidama. Intersections of Intervals and Balls in TOP-REAL n

TOPREALA,

Artur Korni{\l}owicz and Yasunari Shidama. Some Properties of Rectangles on the Plane

TOPREALB,

Artur Korni{\l}owicz and Yasunari Shidama. Some Properties of Circles on the Plane

TOPREALC,

Artur Korni{\l}owicz. On the Continuity of Some Functions

TOPRNS_1,

Agnieszka Sakowicz , Jaros{\l}aw Gryko and Adam Grabowski. Sequences in $R^n$

TOPS_1,

Miros{\l}aw Wysocki and Agata Darmochwa\l. Subsets of Topological Spaces

TOPS_2,

Agata Darmochwa{\l}. Families of Subsets, Subspaces and Mappings in Topological Spaces

TOPS_3,

Zbigniew Karno. Remarks on Special Subsets of Topological Spaces

TOPS_4,

Artur Korni{\l}owicz. Miscellaneous Facts about Open Functions and Continuous Functions

TRANSGEO,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Transformations in Affine Spaces

TRANSLAC,

Henryk Oryszczyszyn and Krzysztof Pra\.zmowski. Translations in Affine Planes

TREAL_1,

Toshihiko Watanabe. The Brouwer Fixed Point Theorem for Intervals

TREES_1,

Grzegorz Bancerek. Introduction to Trees

TREES_2,

Grzegorz Bancerek. K\"onig's Lemma

TREES_3,

Grzegorz Bancerek. Sets and Functions of Trees and Joining Operations of Trees

TREES_4,

Grzegorz Bancerek. Joining of Decorated Trees

TREES_9,

Grzegorz Bancerek. Subtrees

TREES_A,

Oleg Okhotnikov. Replacement of Subtrees in a Tree

TRIANG_1,

Beata Madras. On the concept of the triangulation

TSEP_1,

Zbigniew Karno. Separated and Weakly Separated Subspaces of Topological Spaces

TSEP_2,

Zbigniew Karno. On a Duality Between Weakly Separated Subspaces of Topological Spaces

TSP_1,

Zbigniew Karno. On Kolmogorov Topological Spaces

TSP_2,

Zbigniew Karno. Maximal Kolmogorov Subspaces of a Topological Space as Stone Retracts of the Ambient Space

TURING_1,

Jingchao Chen and Yatsuka Nakamura. Introduction to Turing Machines

TWOSCOMP,

Katsumi Wasaki and Pauline N. Kawamoto. 2's Complement Circuit. Part I. Boolean Operators and 2's Complement Circuit Properties

U

UNIALG_1,

Jaros{\l}aw Kotowicz, Beata Madras and Ma{\l}gorzata Korolkiewicz. Basic Notation of Universal Algebra

UNIALG_2,

Ewa Burakowska. Subalgebras of the Universal Algebra. Lattices of Subalgebras

UNIALG_3,

Miros{\l}aw Jan Paszek. On the Lattice of Subalgebras of a Universal Algebra

UNIFORM1,

Yatsuka Nakamura and Andrzej Trybulec. Lebesgue's Covering Lemma, Uniform Continuity and Segmentation of Arcs

UNIROOTS,

Broderick Arneson and Piotr Rudnicki. Primitive Roots of Unity and Cyclotomic Polynomials

UPROOTS,

Piotr Rudnicki. Little {B}ezout Theorem (Factor Theorem)

URYSOHN1,

J\'ozef Bia\las and Yatsuka Nakamura. Dyadic Numbers and $T_4$ Topological Spaces

URYSOHN2,

J\'ozef Bia{\l}as and Yatsuka Nakamura. Some Properties of Dyadic Numbers and Intervals

URYSOHN3,

J\'ozef Bia{\l}as and Yatsuka Nakamura. Urysohn Lemma

V

VALUAT_1,

Edmund Woronowicz. Interpretation and Satisfiability in the First Order Logic

VALUED_0,

Library Committee. Number-Valued Functions

VALUED_1,

Library Committee. Properties of Number-Valued Functions

VALUED_2,

Artur Korni{\l}owicz. Arithmetic Operations on Functions from Sets into Functional Sets

VECTMETR,

Robert Milewski. Real Linear-Metric Space and Isometric Functions

VECTSP10,

Jaros{\l}aw Kotowicz. Quotient Vector Spaces and Functionals

VECTSP11,

Karol P\c{a}k. Eigenvalues of a Linear Transformation

VECTSP_1,

Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski. Abelian Groups, Fields and Vector Spaces

VECTSP_2,

Micha{\l} Muzalewski. Construction of Rings and Left-, Right-, and Bi-Modules over a Ring

VECTSP_4,

Wojciech A. Trybulec. Subspaces and Cosets of Subspaces in Vector Space

VECTSP_5,

Wojciech A. Trybulec. Operations on Subspaces in Vector Space

VECTSP_6,

Wojciech A. Trybulec. Linear Combinations in Vector Space

VECTSP_7,

Wojciech A. Trybulec. Basis of Vector Space

VECTSP_8,

Andrzej Iwaniuk. On the Lattice of Subspaces of Vector Space

VECTSP_9,

Mariusz \.Zynel. Steinitz Theorem and Dimension of a Vector Space

VFUNCT_1,

Hiroshi Yamazaki and Yasunari Shidama. Algebra of Vector Functions

VFUNCT_2,

Noboru Endou. Algebra of Complex Vector Valued Functions

W

WAYBEL10,

Grzegorz Bancerek. Closure Operators and Subalgebras

WAYBEL11,

Andrzej Trybulec. Scott Topology

WAYBEL12,

Artur Korni{\l}owicz. On the Baire Category Theorem

WAYBEL13,

Robert Milewski. Algebraic and Arithmetic Lattices

WAYBEL14,

Czes{\l}aw Byli\'nski and Piotr Rudnicki. The Scott Topology, Part II

WAYBEL15,

Robert Milewski. More on the Algebraic and Arithmetic Lattices

WAYBEL16,

Robert Milewski. Completely-Irreducible Elements

WAYBEL17,

Adam Grabowski. Scott-Continuous Functions

WAYBEL18,

Jaros{\l}aw Gryko. Injective Spaces

WAYBEL19,

Grzegorz Bancerek. The Lawson Topology

WAYBEL20,

Piotr Rudnicki. Kernel Projections and Quotient Lattices

WAYBEL21,

Grzegorz Bancerek. Lawson Topology in Continuous Lattices

WAYBEL22,

Piotr Rudnicki. Representation theorem for free continuous lattices

WAYBEL23,

Robert Milewski. Bases of Continuous Lattices

WAYBEL24,

Adam Grabowski. Scott-Continuous Functions, Part II

WAYBEL25,

Artur Korni{\l}owicz and Jaros{\l}aw Gryko. Injective Spaces, Part { II }

WAYBEL26,

Grzegorz Bancerek. Continuous Lattices between T$_0$ Spaces

WAYBEL27,

Grzegorz Bancerek and Adam Naumowicz. Function Spaces in the Category of Directed Suprema Preserving Maps

WAYBEL28,

Bart{\l}omiej Skorulski. Lim-inf Convergence

WAYBEL29,

Grzegorz Bancerek and Adam Naumowicz. The Characterization of Continuity of Topologies

WAYBEL30,

Artur Korni{\l}owicz. Meet Continuous Lattices Revisited

WAYBEL31,

Robert Milewski. Weights of Continuous Lattices

WAYBEL32,

Ewa Gr\c{a}dzka. On the Order-consistent Topology of Complete and Uncomplete Lattices

WAYBEL33,

Grzegorz Bancerek and Noboru Endou. Compactness of Lim-inf Topology

WAYBEL34,

Grzegorz Bancerek. Duality Based on Galois Connection. Part I

WAYBEL35,

Artur Korni{\l}owicz. Morphisms Into Chains, Part {I}

WAYBEL_0,

Grzegorz Bancerek. Directed Sets, Nets, Ideals, Filters, and Maps

WAYBEL_1,

Czes\law Byli\'nski. Galois Connections

WAYBEL_2,

Artur Korni{\l}owicz. Meet-continuous Lattices

WAYBEL_3,

Grzegorz Bancerek. The "Way-Below" Relation

WAYBEL_4,

Adam Grabowski. Auxiliary and Approximating Relations

WAYBEL_5,

Mariusz \.Zynel. The Equational Characterization of Continuous Lattices

WAYBEL_6,

Beata Madras. Irreducible and Prime Elements

WAYBEL_7,

Grzegorz Bancerek. Prime Ideals and Filters

WAYBEL_8,

Robert Milewski. Algebraic Lattices

WAYBEL_9,

Artur Korni{\l}owicz. On The Topological Properties of Meet-Continuous Lattices

WEDDWITT,

Broderick Arneson , Matthias Baaz and Piotr Rudnicki. Witt's Proof of the {W}edderburn Theorem

WEIERSTR,

J\'ozef Bia\las and Yatsuka Nakamura. The Theorem of Weierstrass

WELLFND1,

Piotr Rudnicki and Andrzej Trybulec. On same equivalents of well-foundedness

WELLORD1,

Grzegorz Bancerek. The Well Ordering Relations

WELLORD2,

Grzegorz Bancerek. Zermelo Theorem and Axiom of Choice. The correspondence of well ordering relations and ordinal numbers

WELLSET1,

Bogdan Nowak and S{\l}awomir Bia{\l}ecki. Zermelo's Theorem

WSIERP_1,

Andrzej Kondracki. The Chinese Remainder Theorem

X

XBOOLE_0,

Library Committee. Boolean Properties of Sets - Definitions

XBOOLE_1,

Library Committee. Boolean Properties of Sets - Theorems

XBOOLEAN,

Library Committee. On the Arithmetic of Boolean Values

XCMPLX_0,

Library Committee. Complex Numbers - Basic Definitions

XCMPLX_1,

Library Committee. Complex Numbers - Basic Theorems

XREAL_0,

Library Committee. Introduction to Arithmetic of Real Numbers

XREAL_1,

Library Committee. Real Numbers - Basic Theorems

XXREAL_0,

Library Committee. Introduction to Arithmetic of Extended Real Numbers

XXREAL_1,

Andrzej Trybulec, Yatsuka Nakamura, Artur Korni{\l}owicz and. Basic Properties of Extended Real Numbers

XXREAL_2,

Andrzej Trybulec. Suprema and Infima of Intervals of Extended Real Numbers

XXREAL_3,

Andrzej Trybulec. Basic Operations on Extended Real Numbers

Y

YELLOW10,

Artur Korni{\l}owicz. The Properties of Product of Relational Structures

YELLOW11,

Adam Naumowicz. On the Characterization of Modular and Distributive Lattices

YELLOW12,

Artur Korni{\l}owicz. On the Characterization of {H}ausdorff Spaces

YELLOW13,

Artur Korni{\l}owicz. Introduction to Meet-Continuous Topological Lattices

YELLOW14,

Jaros{\l}aw Gryko and Artur Korni{\l}owicz. Some Properties of Isomorphism between Relational Structures. On the Product of Topological Spaces

YELLOW15,

Robert Milewski. Components and Basis of Topological Spaces

YELLOW16,

Grzegorz Bancerek. Retracts and Inheritance

YELLOW17,

Bart{\l}omiej Skorulski. The Tichonov Theorem

YELLOW18,

Grzegorz Bancerek. Concrete Categories

YELLOW19,

Grzegorz Bancerek , Noboru Endou and Yuji Sakai. On the characterizations of compactness

YELLOW20,

Grzegorz Bancerek. Miscellaneous Facts about Functors

YELLOW21,

Grzegorz Bancerek. Categorial Background for Duality Theory

YELLOW_0,

Grzegorz Bancerek. Bounds in Posets and Relational Substructures

YELLOW_1,

Adam Grabowski and Robert Milewski. Boolean Posets, Posets under Inclusion and Products of Relational Structures

YELLOW_2,

Mariusz \.Zynel and Czes{\l}aw Byli\'nski. Properties of Relational Structures, Posets, Lattices and Maps

YELLOW_3,

Artur Korni{\l}owicz. Cartesian Products of Relations and Relational Structures

YELLOW_4,

Artur Korni{\l}owicz. Definitions and Properties of the Join and Meet of Subsets

YELLOW_5,

Agnieszka Julia Marasik. Miscellaneous Facts about Relation Structure

YELLOW_6,

Andrzej Trybulec. Moore-Smith Convergence

YELLOW_7,

Grzegorz Bancerek. Duality in Relation Structures

YELLOW_8,

Andrzej Trybulec. Baire Spaces, Sober Spaces

YELLOW_9,

Grzegorz Bancerek. Bases and Refinements of Topologies

YONEDA_1,

Miros{\l}aw Wojciechowski. Yoneda Embedding

Z

ZF_COLLA,

Grzegorz Bancerek. The Contraction Lemma

ZF_FUND1,

Andrzej Kondracki. Mostowski's Fundamental Operations - Part I

ZF_FUND2,

Grzegorz Bancerek and Andrzej Kondracki. Mostowski's Fundamental Operations - Part II

ZF_LANG,

Grzegorz Bancerek. A Model of ZF Set Theory Language

ZF_LANG1,

Grzegorz Bancerek. Replacing of Variables in Formulas of ZF Theory

ZF_MODEL,

Grzegorz Bancerek. Models and Satisfiability. Defining by Structural Induction and Free Variables in ZF-formulae

ZF_REFLE,

Grzegorz Bancerek. The Reflection Theorem

ZFMISC_1,

Czes{\l}aw Byli\'nski. Some Basic Properties of Sets

ZFMODEL1,

Grzegorz Bancerek. Properties of ZF Models

ZFMODEL2,

Grzegorz Bancerek. Definable Functions

ZFREFLE1,

Grzegorz Bancerek. Consequences of the Reflection Theorem