# General Topology

Springer Science & Business Media, Jun 27, 1975 - Mathematics - 298 pages

Aimed at graduate math students, this classic work is a systematic exposition of general topology and is intended to be a reference and a text. As a reference, it offers a reasonably complete coverage of the area, resulting in a more extended treatment than normally given in a course. As a text, the exposition in the earlier chapters proceeds at a pedestrian pace. A preliminary chapter covers those topics requisite to the main body of work.

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#### LibraryThing Review

User Review  - trurl - LibraryThing

There are two introductions to general topology which are classics. Thsi book, Kelley, is the lighter one of them, while Engelking is the heavier one. Read full review

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Book a bit old. The concept of filtre or ultrafiltre is not addressed. Filtres are very powerful tools and using ultrafiltres, we can define hyperreal numbers.

### Contents

 PRELIMINARIES 1 UNION AND INTERSECTION 2 RELATIONS 6 FUNCTIONS 10 ORDERINGS 13 ALGEBRAIC CONCEPTS 17 THE REAL NUMBERS 19 COUNTABLE SETS 25
 QUOTIENT SPACES 147 COMPACTIFICATION 149 LEBESGUPS COHERING LEMMA 154 PARACOMPACTNESS 156 PROBLEMS 161 UNIFORM SPACES 174 UNIFORMITIES AND THE UNIFORM TOPOLOGY 175 UNIFORM CONTINUITY PRODUCT UNIFORMITIES 180

 CARDINAL NUMBERS 27 ORDINAL NUMBERS 29 CARTESIAN PRODUCTS 30 HAUSDORFF MAXIMAL PRINCIPLE 31 TOPOLOGICAL SPACES 37 CLOSED SETS 40 CLOSURE 42 BASES AND SUBBASES 46 CONNECTED SETS 53 PROBLEMS 55 MOORESMITH CONVERGENCE 62 SUBNETS AND CLUSTER POINTS 69 SEQUENCES AND SUBSEQUENCES 72 CONVERGENCECLASSES 73 PROBLEMS 76 PRODUCT AND QUOTIENT SPACES 84 PRODUCT SPACES 88 QUOTIENT SPACES 94 PROBLEMS 100 EMBEDDING AND METRIZATION 111 EMBEDDING IN CUBES 115 METRIC AND PSEUDOMETRIC SPACES 118 METRIZATION 124 PROBLEMS 130 COMPACT SPACES 135 PRODUCTS OF COMPACT SPACES 143 LOCALLY COMPACT SPACES 146
 METRIZATION 184 COMPLETENESS 190 COMPLETION 195 COMPACT SPACES 197 FOR METRIC SPACES ONLY 200 PROBLEMS 203 FUNCTION SPACES 217 COMPACT OPEN TOPOLOGY AND JOINT CONTINUITY 221 UNIFORM CONVERGENCE 225 UNIFORM CONVERGENCE ON COMPACTA 229 COMPACTNESS AND EQUICONTINUITY 231 EVEN CONTINUITY 234 PROBLEMS 238 ELEMENTARY SET THEORY 250 THE CLASSIFICATION AXIOM SCHEME 251 EXISTENCE OF SETS 256 RELATIONS 259 FUNCTIONS 260 WELL ORDERING 262 ORDINALS 266 INTEGERS 271 THE CHOICE AXIOM 272 CARDINAL NUMBERS 274 Bibliography 282 INDEX 293 Copyright