General Topology

By: STEPHEN WILLARD

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Paperback | 27 February 2004

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384 Pages

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12.7 x 17.3 x 27.9

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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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Non-Fiction Mathematics Topology

Set Theory and Metric Spaces
Set theory	p. 1
Metric spaces	p. 15
Topological Spaces
Fundamental concepts	p. 23
Neighborhoods	p. 31
Bases and subbases	p. 36
New Spaces from Old
Subspaces	p. 41
Continuous functions	p. 44
Product spaces; weak topologies	p. 52
Quotient spaces	p. 59
Convergence
Inadequacy of sequences	p. 70
Nets	p. 73
Filters	p. 77
Separation and Countability
The separation axioms	p. 85
Regularity and complete regularity	p. 92
Normal spaces	p. 99
Countability properties	p. 108
Compactness
Compact spaces	p. 116
Locally compact spaces	p. 129
Compactification	p. 135
Paracompactness	p. 144
Products of normal spaces	p. 155
Metrizable Spaces
Metric spaces and metrizable spaces	p. 161
Metrization	p. 165
Complete metric spaces	p. 175
The Baire theorem	p. 185
Connectedness
Connected spaces	p. 191
Pathwise and local connectedness	p. 197
Continua	p. 203
Totally disconnected spaces	p. 210
The Cantor set	p. 216
Peano spaces	p. 219
The homotopy relation	p. 222
The fundamental group	p. 227
II[subscript 1](S[superscript 1])	p. 233
Uniform Spaces
Diagonal uniformities	p. 238
Uniform covers	p. 244
Uniform products and subspaces; weak uniformities	p. 251
Uniformizability and uniform metrizability	p. 255
Complete uniform spaces; completion	p. 260
Proximity spaces	p. 266
Compactness and proximities	p. 273
Function Spaces
Pointwise convergence; uniform convergence	p. 278
The compact-open topology and uniform convergence on compacta	p. 282
The Stone-Weierstrass theorem	p. 290
Historical Notes	p. 297
Bibliography	p. 323
Index	p. 345
Table of Contents provided by Ingram. All Rights Reserved.

General Topology

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