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
FOO5,
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
GOO,
Article Author. Article Title
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