Encyclopedia of General Topology
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Table of contents
- Cover
- Contentsv
- Prefacevii
- Contributorsix
- Chapter A. Generalities1
- a-01 Topological Spaces3
- a-02 Modified Open and Closed Sets (Semi-Open Set etc.)8
- a-03 Cardinal Functions, Part I11
- a-04 Cardinal Functions, Part II15
- a-05 Convergence18
- a-06 Several Topologies on One Set22
- a-07 Comparison of Topologies (Minimal and Maximal Topologies)24
- Chapter B. Basic constructions29
- b-01 Subspaces (Hereditary (P)-Spaces)31
- b-02 Relative Properties33
- b-03 Product Spaces37
- b-04 Quotient Spaces and Decompositions43
- b-05 Adjunction Spaces47
- b-06 Hyperspaces49
- b-07 Cleavable (Splittable) Spaces53
- b-08 Inverse Systems and Direct Systems56
- b-09 Covering Properties60
- b-10 Locally (P)-Spaces65
- b-11 Rim(P)-Spaces67
- b-12 Categorical Topology74
- b-13 Special Spaces76
- Chapter C. Maps and general types of spaces defined by maps81
- c-01 Continuous and Topological Mappings83
- c-02 Open Maps86
- c-03 Closed Maps89
- c-04 Perfect Maps92
- c-05 Cell-Like Maps97
- c-06 Extensions of Maps100
- c-07 Topological Embeddings (Universal Spaces)103
- c-08 Continuous Selections107
- c-09 Multivalued Functions110
- c-10 Applications of the Baire Category Theorem to Real Analysis113
- c-11 Absolute Retracts117
- c-12 Extensors122
- c-13 Generalized Continuities126
- c-14 Spaces of Functions in Pointwise Convergence131
- c-15 Radon–Nikodým Compacta138
- c-16 Corson Compacta140
- c-17 Rosenthal Compacta142
- c-18 Eberlein Compacta145
- c-19 Topological Entropy147
- c-20 Function Spaces150
- Chapter D. Fairly general properties153
- d-01 The Low Separation Axioms T0 and T1155
- d-02 Higher Separation Axioms158
- d-03 Fréchet and Sequential Spaces162
- d-04 Pseudoradial Spaces165
- d-05 Compactness (Local Compactness, Sigma-Compactness etc.)169
- d-06 Countable Compactness174
- d-07 Pseudocompact Spaces177
- d-08 The Lindelöf Property182
- d-09 Realcompactness185
- d-10 k-Spaces189
- d-11 Dyadic Compacta192
- d-12 Paracompact Spaces195
- d-13 Generalizations of Paracompactness198
- d-14 Countable Paracompactness, Countable Metacompactness, and Related Concepts202
- d-15 Extensions of Topological Spaces204
- d-16 Remainders208
- d-17 The Cech–Stone Compactification210
- d-18 The Cech–Stone Compactifications213
- d-19 Wallman–Shanin Compactification218
- d-20 H-Closed Spaces221
- d-21 Connectedness223
- d-22 Connectifications227
- d-23 Special Constructions229
- Chapter E. Spaces with richer structures233
- e-01 Metric Spaces235
- e-02 Classical Metrization Theorems239
- e-03 Modern Metrization Theorems242
- e-04 Special Metrics247
- e-05 Completeness251
- e-06 Baire Spaces255
- e-07 Uniform Spaces, I259
- e-08 Uniform Spaces, II264
- e-09 Quasi-Uniform Spaces266
- e-10 Proximity Spaces271
- e-11 Generalized Metric Spaces, Part I273
- e-12 Generalized Metric Spaces, Part II276
- e-13 Generalized Metric Spaces III. Linearly Stratifiable Spaces and Analogous Classes of Spaces281
- e-14 Monotone Normality286
- e-15 Probabilistic Metric Spaces288
- e-16 Approach Spaces293
- Chapter F. Special properties297
- f-01 Continuum Theory299
- f-02 Continuum Theory (General)304
- f-03 Dimension Theory (General Theory)308
- f-04 Dimension of Metrizable Spaces314
- f-05 Dimension Theory: Infinite Dimension318
- f-06 Zero-Dimensional Spaces323
- f-07 Linearly Ordered and Generalized Ordered Spaces326
- f-08 Unicoherence and Multicoherence331
- f-09 Topological Characterizations of Separable Metrizable Zero-Dimensional Spaces334
- f-10 Topological Characterizations of Spaces337
- f-11 Higher-Dimensional Local Connectedness341
- Chapter G. Special spaces343
- g-01 Extremally Disconnected Spaces345
- g-02 Scattered Spaces350
- g-03 Dowker Spaces354
- Chapter H. Connections with other structures357
- h-01 Topological Groups359
- h-02 TopologicalRings, Division Rings, Fields and Lattices365
- h-03 Free Topological Groups372
- h-04 Homogeneous Spaces376
- h-05 TransformationGroups and Semigroups379
- h-06 Topological Discrete Dynamical Systems385
- h-07 Fixed Point Theorems402
- h-08 Topological Representations of Algebraic Systems409
- Chapter J. Influences of other fields415
- j-01 Descriptive Set Theory417
- j-02 Consistency Results in Topology, I: Quotable Principles419
- j-03 Consistency Results in Topology, II: Forcing and Large Cardinals423
- j-04 Digital Topology428
- j-05 Computer Science and Topology433
- j-06 Non Standard Topology436
- j-07 Topological Games439
- j-08 Fuzzy Topological Spaces443
- Chapter K. Connections with other fields447
- k-01 Banach Spaces and Topology (I)449
- k-02 Banach Spaces (and Topology) (II)454
- k-03 Measure Theory, I459
- k-04 Measure Theory, II464
- k-05 Polyhedra and Complexes470
- k-06 Homology474
- k-07 Homotopy, I480
- k-08 Homotopy, II485
- k-09 Shape Theory489
- k-10 Manifold494
- k-11 Infinite-Dimensional Topology497
- Subject index503
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