rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Introduction to set theory and topology
  title info:
    title: Wstęp do teorii mnogości i topologii. English
  name:
    name part: Kuratowski, Kazimierz
    name part: 1896-1980
    role:
      role term: creator
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: enk
    date issued: 1972
    edition: Completely revised 2d English edition. /
    issuance: monographic
  language:
    language term: eng
  language:
    language term: pol
  physical description:
    form: remote
    extent: 1 online resource (352 pages) : illustrations
  abstract: 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.
  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.
  table of contents: 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.
  table of contents: 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.
  table of contents: 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.
  note: by Kazimierz Kuratowski. Containing a suppl. on Elements of algebraic topology, by Ryszard Engelking.
  note: Translation of Wstęp do teorii mnogości i topologii.
  note: 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
  note: digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references and index.
  subject:
    topic: Set theory
  subject:
    topic: Topology
  subject:
    topic: Théorie des ensembles
  subject:
    topic: Topologie
  subject:
    topic: MATHEMATICS
    topic: Topology
  subject:
    topic: Set theory
  subject:
    topic: Topology
  subject:
    topic: Verzamelingen (wiskunde)
  subject:
    topic: Topologie
  subject:
    topic: Topological spaces
  subject:
    topic: Mathematics
    topic: Sets
  classification: QA248 .K7693 1972eb
  classification: 514/.3
  classification: 31.10
  classification: 31.60
  related item:
    title info:
      title: Elements of algebraic topology
    name:
      name part: Engelking, Ryszard.
  related item:
    title info:
      title: Introduction to set theory and topology
    title info:
      title: Wstęp do teorii mnogości i topologii. English
    name:
      name part: Kuratowski, Kazimierz, 1896-1980.
    origin info:
      edition: Completely revised 2d English edition
    identifier: (DLC) 72149123
    identifier: (OCoLC)508535
  related item:
    title info:
      title: International series of monographs in pure and applied mathematics ; v. 101
  identifier: 9781483151632
  identifier: 1483151638
  identifier: 008016160X
  identifier: 9780080161600
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OPELS
    record creation date: 141027
    record change date: 20260326211534.5
    record identifier: in00005757412
    language of cataloging:
      language term: eng