Introduction to set theory and topology
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.
Read More ↓Title Statements
- Full title :Introduction to set theory and topology / by Kazimierz Kuratowski. Containing a suppl. on Elements of algebraic topology, by Ryszard Engelking.
Summary
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.
Read More ↓Edition Statements
- Publication Date:1972
- Edition:Completely revised 2d English edition
Publication Statements
- Publisher(s):Pergamon Press
- Place of Publication:Oxford
- Language:eng
- Publication Date:1972
Notes
Translation of Wstęp do teorii mnogości i topologii.
The Physical Object
- Description:1 online resource (352 pages) : : illustrations
Edition Identifiers
- ISBN:9781483151632, 1483151638
- oclc:ocn893872962
- LC Classification:QA248
- Dewey Decimal:514/.3
Table of Contents
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 set…
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