General Topology

Front Cover
Courier Corporation, 2004 - 369 pages
7 Reviews
Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and "geometric topology," covered by nine sections on connectivity properties, topological characterization theorems, and homotopy theory. Many standard spaces are introduced in the related problems that accompany each section (340 exercises in all). The text's value as a reference work is enhanced by a collection of historical notes, a bibliography, and index. 1970 edition. 27 figures.
  

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It is clear in it's definitions of topology spaces, more especially with the closure and interior properties. It's a must read for all those aspiring mathematicians out there with the knowledge of set theory who like to advance to more rigorous fields of analysis.

Contents

Chapter
1
Inadequacy of sequences
70
Compact spaces
116
23
144
52
152
59
159
Metrizable Spaces 22 Metric spaces and metrizable spaces
161
Metrization
163
The homotopy relation
222
The fundamental group
227
FMS
233
Uniform Spaces 35 Diagonal uniforrnities
238
Uniform covers
244
Uniform products and subspaces weak uniforrnities
251
Uniforinizability and uniform metrizability
255
Complete unifonn spaces completion
260

70
170
Complete metric spaces
179
The Baire theorem
188
Connectedness 26 Connected spaces
191
85
192
Pathwise and local connectedness
199
Continua
203
Totally disconnected spaces
213
The Cantor set
218
3l Peano spaces
219
Proximity spaces
266
4l Compactness and proximities
273
Chapter I0 Function Spaces 42 Pointwise convergence uniform convergence
278
The compactopen topology and uniform convergence on compacta
282
The StoneWeierstrass theorem
290
Historical Notes
297
Bibliography
323
Index
345
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