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Wstęp do teorii mnogości i topologii. English
Completely revised 2d English edition. /
1 online resource (352 pages) : illustrations
Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered.
Front Cover; Introduction to Set Theory and Topology; Copyright Page; Table of Contents; FOREWORD TO THE FIRST ENGLISH EDITION; FOREWORD TO THE SECOND ENGLISH EDITION; Part I: SET THEORY; INTRODUCTION TO PART I; CHAPTER I. PROPOSITIONAL CALCULUS; 1. The disjunction and conjunction of propositions; 2. Negation; 3. Implication; Exercises; CHAPTER II. ALGEBRA OF SETS. FINITE OPERATIONS; 1. Operations on sets; 2. Inter-relationship with the propositional calculus; 3. Inclusion; 4. Space. Complement of a set; 5. The axiomatics of the algebra of sets; 6. Boolean algebra.+ Lattices.
7. Ideals and filtersExercises; CHAPTER III. PROPOSITIONAL FUNCTIONS. CARTESIAN PRODUCTS; 1. The operation; 2. Quantifiers; 3. Ordered pairs; 4. Cartesian product; 5. Propositional functions of two variables. Relations; 6. Cartesian products of n sets. Propositional functions of n variables; 7. On the axiomatics of set theory; Exercises; CHAPTER IV. THE MAPPING CONCEPT. INFINITE OPERATIONS. FAMILIES OF SETS; 1. The mapping concept; 2. Set-valued mappings; 3. The mapping; 4. Images and inverse images determined by a mapping; 5· The operations U R and)"R. Covers.
6. Additive and multiplicative families of sets7. Borel families of sets; 8. Generalized cartesian products; Exercises; CHAPTER V. THE CONCEPT OF THE POWER OF A SET. COUNTABLESETS; 1. One-to-one mappings; 2. Power of a set; 3. Countable sets; Exercises; CHAPTER VI. OPERATIONS ON CARDINAL NUMBERS. THE NUMBERS a AND c; 1. Addition and multiplication; 2. Exponentiation; 3. Inequalities for cardinal numbers; 4. Properties of the number c; Exercises; CHAPTER VII. ORDER RELATIONS; 1. Definitions; 2. Similarity. Order types; 3. Dense ordering; 4. Continuous ordering; Exercises.
7. Uniform convergenceExercises; CHAPTER X. TOPOLOGICAL SPACES; 1. Definition. Closure axioms; 2. Relations to metric spaces; 3. Further algebraic properties of the closure operation; 4. Closed sets. Open sets; 5. Operations on closed sets and open sets; 6. Interior points. Neighbourhoods; 7. The concept of open set as the primitive term of the notion of topological space; 8. Base and subbase; 9. Relativization. Subspaces; 10. Comparison of topologies; 11. Cover of a space; Exercises; CHAPTER XI. BASIC TOPOLOGICAL CONCEPTS; 1. Borel sets; 2. Dense sets and boundary sets.
by Kazimierz Kuratowski. Containing a suppl. on Elements of algebraic topology, by Ryszard Engelking.
Translation of Wstęp do teorii mnogości i topologii.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
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Includes bibliographical references and index.
International series of monographs in pure and applied mathematics ; v. 101