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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 d...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Polaco |
| Publicado: |
Oxford ; New York :
Pergamon Press,
[1972]
|
| Edición: | Completely revised 2d English edition. / |
| Colección: | International series of monographs in pure and applied mathematics ;
v. 101. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 001 | SCIDIR_ocn893872962 | ||
| 003 | OCoLC | ||
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| 100 | 1 | |a Kuratowski, Kazimierz, |d 1896-1980. | |
| 240 | 1 | 0 | |a Wst�ep do teorii mnogo�sci i topologii. |l English |
| 245 | 1 | 0 | |a Introduction to set theory and topology / |c by Kazimierz Kuratowski. Containing a suppl. on Elements of algebraic topology, by Ryszard Engelking. |
| 250 | |a Completely revised 2d English edition. / |b Translated from Polish by Leo F. Boro�n. | ||
| 264 | 1 | |a Oxford ; |a New York : |b Pergamon Press, |c [1972] | |
| 300 | |a 1 online resource (352 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a International series of monographs in pure and applied mathematics ; |v volume 101 | |
| 500 | |a Translation of Wst�ep do teorii mnogo�sci i topologii. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 546 | |a Translation of Wst�ep do teorii mnogo�sci i topologii. | ||
| 520 | |a 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. | ||
| 588 | 0 | |a Print version record. | |
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2011. |5 MiAaHDL | ||
| 538 | |a 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. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2011 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |6 880-01 |a 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. | |
| 650 | 0 | |a Set theory. | |
| 650 | 0 | |a Topology. | |
| 650 | 6 | |a Th�eorie des ensembles. |0 (CaQQLa)201-0001167 | |
| 650 | 6 | |a Topologie. |0 (CaQQLa)201-0001193 | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Set theory. |2 fast |0 (OCoLC)fst01113587 | |
| 650 | 7 | |a Topology. |2 fast |0 (OCoLC)fst01152692 | |
| 650 | 1 | 7 | |a Verzamelingen (wiskunde) |2 gtt |
| 650 | 1 | 7 | |a Topologie. |2 gtt |
| 653 | |a Topological spaces | ||
| 653 | |a Mathematics |a Sets | ||
| 700 | 1 | 2 | |a Engelking, Ryszard. |t Elements of algebraic topology. |
| 776 | 0 | 8 | |i Print version: |a Kuratowski, Kazimierz, 1896-1980. |s Wst�ep do teorii mnogo�sci i topologii. English. |t Introduction to set theory and topology. |b Completely revised 2d English edition |z 008016160X |w (DLC) 72149123 |w (OCoLC)508535 |
| 830 | 0 | |a International series of monographs in pure and applied mathematics ; |v v. 101. | |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780080161600 |z Texto completo |
| 880 | 8 | |6 505-01/(S |a CHAPTER VIII. WELL ORDERING1. Well ordering; 2. Theorem on transfinite induction; 3. Theorems on the comparison of ordinal numbers; 4. Sets of ordinal numbers; 5. The number Ω; 6. The arithmetic of ordinal numbers; 7. The well-ordering theorem; 8. Definitions by transfinite induction; Exercises; Part II: TOPOLOGY; INTRODUCTION TO PART II; CHAPTER IX. METRIC SPACES. EUCLIDEAN SPACES; 1. Metric spaces; 2. Diameter of a set. Bounded spaces. Bounded mappings; 3. The Hubert cube; 4. Convergence of a sequence of points; 5. Properties of the limit; 6. Limit in the cartesian product. | |