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Encyclopedia of General Topology - J.E. Vaughn

Encyclopedia of General Topology

Hardcover

Published: 18th November 2003
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This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.


Key features:


- More terms from General Topology than any other book ever published
- Short and informative articles
- Authors include the majority of top researchers in the field
- Extensive indexing of terms

The book will be very useful for the mathematical community. Ljubisa Kocinac (Aleksandrovac). Mathematical Reviews, 2005

Preface
Contributors
Generalities
Topological Spacesp. 3
Modified Open and Closed Sets (Semi-Open Set etc.)p. 8
Cardinal Functions, Part Ip. 11
Cardinal Functions, Part IIp. 15
Convergencep. 18
Several Topologies on One Setp. 22
Comparison of Topologies (Minimal and Maximal Topologies)p. 24
Basic constructions
Subspaces (Hereditary (P)-Spaces)p. 31
Relative Propertiesp. 33
Product Spacesp. 37
Quotient Spaces and Decompositionsp. 43
Adjunction Spacesp. 47
Hyperspacesp. 49
Cleavable (Splittable) Spacesp. 53
Inverse Systems and Direct Systemsp. 56
Covering Propertiesp. 60
Locally (P)-Spacesp. 65
Rim(P)-Spacesp. 67
Categorical Topologyp. 74
Special Spacesp. 76
Maps and general types of spaces defined by maps
Continuous and Topological Mappingsp. 83
Open Mapsp. 86
Closed Mapsp. 89
Perfect Mapsp. 92
Cell-Like Mapsp. 97
Extensions of Mapsp. 100
Topological Embeddings (Universal Spaces)p. 103
Continuous Selectionsp. 107
Multivalued Functionsp. 110
Applications of the Baire Category Theorem to Real Analysisp. 113
Absolute Retractsp. 117
Extensionsp. 122
Generalized Continuitiesp. 126
Spaces of Functions in Pointwise Convergencep. 131
Radon-Nikodym Compactap. 138
Corson Compactap. 140
Rosenthal Compactap. 142
Eberlein Compactap. 145
Topological Entropyp. 147
Function Spacesp. 150
Fairly general properties
The Low Separation Axioms T[subscript 0] and T[subscript 1]p. 155
Higher Separation Axiomsp. 158
Frechet and Sequential Spacesp. 162
Pseudoradial Spacesp. 165
Compactness (Local Compactness, Sigma-Compactness etc.)p. 169
Countable Compactnessp. 174
Pseudocompact Spacesp. 177
The Lindelof Propertyp. 182
Realcompactnessp. 185
[kappa]-Spacesp. 189
Dyadic Compactap. 192
Paracompact Spacesp. 195
Generalizations of Paracompactnessp. 198
Countable Paracompactness, Countable Metacompactness, and Related Conceptsp. 202
Extensions of Topological Spacesp. 204
Remaindersp. 208
The Cech-Stone Compactificationp. 210
The Cech-Stone Compactifications of N and Rp. 213
Wallman-Shanin Compactificationp. 218
H-Closed Spacesp. 221
Connectednessp. 223
Connectificationsp. 227
Special Constructionsp. 229
Spaces with richer structures
Metric Spacesp. 235
Classical Metrization Theoremsp. 239
Modern Metrization Theoremsp. 242
Special Metricsp. 247
Completenessp. 251
Baire Spacesp. 255
Uniform Spaces, Ip. 259
Uniform Spaces, IIp. 264
Quasi-Uniform Spacesp. 266
Proximity Spacesp. 271
Generalized Metric Spaces, Part Ip. 273
Generalized Metric Spaces, Part IIp. 276
Generalized Metric Spaces III: Linearly Stratifiable Spaces and Analogous Classes of Spacesp. 281
Monotone Normalityp. 286
Probabilistic Metric Spacesp. 288
Approach Spacesp. 293
Special properties
Continuum Theoryp. 299
Continuum Theory (General)p. 304
Dimension Theory (General Theory)p. 308
Dimension of Metrizable Spacesp. 314
Dimension Theory: Infinite Dimensionp. 318
Zero-Dimensional Spacesp. 323
Linearly Ordered and Generalized Ordered Spacesp. 326
Unicoherence and Multicoherencep. 331
Topological Characterizations of Separable Metrizable Zero-Dimensional Spacesp. 334
Topological Characterizations of Spacesp. 337
Higher-Dimensional Local Connectednessp. 341
Special spaces
Extremally Disconnected Spacesp. 345
Scattered Spacesp. 350
Dowker Spacesp. 354
Connections with other structures
Topological Groupsp. 359
Topological Rings, Division Rings, Fields and Latticesp. 365
Free Topological Groupsp. 372
Homogeneous Spacesp. 376
Transformation Groups and Semigroupsp. 379
Topological Discrete Dynamical Systemsp. 385
Fixed Point Theoremsp. 402
Topological Representations of Algebraic Systemsp. 409
Influencies of other fields
Descriptive Set Theoryp. 417
Consistency Results in Topology, I: Quotable Principlesp. 419
Consistency Results in Topology, II: Forcing and Large Cardinalsp. 423
Digital Topologyp. 428
Computer Science and Topologyp. 433
Non Standard Topologyp. 436
Topological Gamesp. 439
Fuzzy Topological Spacesp. 443
Connections with other fields
Banach Spaces and Topology (I)p. 449
Banach Spaces (and Topology) (II)p. 454
Measure Theory, Ip. 459
Measure Theory, IIp. 464
Polyhedra and Complexesp. 470
Homologyp. 474
Homotopy, Ip. 480
Homotopy, IIp. 485
Shape Theoryp. 489
Manifoldp. 494
Infinite-Dimensional Topologyp. 497
Subject indexp. 503
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780444503558
ISBN-10: 0444503552
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 536
Published: 18th November 2003
Publisher: Elsevier Science & Technology
Country of Publication: GB
Dimensions (cm): 21.6 x 27.9  x 2.64
Weight (kg): 1.64