General Topology

Front Cover
Springer Science & Business Media, Jun 27, 1975 - Mathematics - 298 pages
6 Reviews

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.

 

What people are saying - Write a review

User ratings

5 stars
5
4 stars
0
3 stars
1
2 stars
0
1 star
0

User Review - Flag as inappropriate

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.

User Review - Flag as inappropriate

great book

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

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information