Table of Contents

PrefaceContributorsA Generalities a-01 Topological Spaces a-02 Modified Open and Closed Sets (Semi-Open Set etc.) a-03 Cardinal Functions, Part I a-04 Cardinal Functions, Part II a-05 Convergence a-06 Several Topologies on One Set a-07 Comparison of Topologies (Minimal and Maximal Topologies)B Basic constructions b-01 Subspaces (Hereditary (P)-Spaces) b-02 Relative Properties b-03 Product Spaces b-04 Quotient Spaces and Decompositions b-05 Adjunction Spaces b-06 Hyperspaces b-07 Cleavable (Splittable) Spaces b-08 Inverse Systems and Direct Systems b-09 Covering Properties b-10 Locally (P)-Spaces b-11 Rim(P)-Spaces b-12 Categorical Topology b-13 Special SpacesC Maps and general types of spaces defined by maps c-01 Continuous and Topological Mappings c-02 Open Maps c-03 Closed Maps c-04 Perfect Maps c-05 Cell-Like Maps c-06 Extensions of Maps c-07 Topological Embeddings (Universal Spaces) c-08 Continuous Selections c-09 Multivalued Functions c-10 Applications of the Baire Category Theorem to Real Analysis c-11 Absolute Retracts c-12 Extensors c-13 Generalized Continuities c-14 Spaces of Functions in Pointwise Convergence c-15 Radon-Nikodym Compacta c-16 Corson Compacta c-17 Rosenthal Compacta c-18 Eberlein Compacta c-19 Topological Entropy c-20 Function SpacesD Fairly general properties d-01 The Low Separation Axioms T0 and T1 d-02 Higher Separation Axioms d-03 Fréchet and Sequential Spaces d-04 Pseudoradial Spaces d-05 Compactness (Local Compactness, Sigma-Compactness etc.) d-06 Countable Compactness d-07 Pseudocompact Spaces d-08 The Lindelöf Property d-09 Realcompactness d-10 k-Spaces d-11 Dyadic Compacta d-12 Paracompact Spaces d-13 Generalizations of Paracompactness d-14 Countable Paracompactness, Countable Metacompactness, and Related Concepts d-15 Extensions of Topological Spaces d-16 Remainders d-17 The Cech-Stone Compactification d-18 The Cech-Stone Compactifications of N and R d-19 Wallman-Shanin Compactification d-20 H-Closed Spaces d-21 Connectedness d-22 Connectifications d-23 Special ConstructionsE Spaces with richer structures e-01 Metric Spaces e-02 Classical Metrization Theorems e-03 Modern Metrization Theorems e-04 Special Metrics e-05 Completeness e-06 Baire Spaces e-07 Uniform Spaces, I e-08 Uniform Spaces, II e-09 Quasi-Uniform Spaces e-10 Proximity Spaces e-11 Generalized Metric Spaces, Part I e-12 Generalized Metric Spaces, Part II e-13 Generalized Metric Spaces III: Linearly Stratifiable Spaces and Analogous Classes of Spaces e-14 Monotone Normality e-15 Probabilistic Metric Spaces e-16 Approach SpacesF Special properties f-01 Continuum Theory f-02 Continuum Theory (General) f-03 Dimension Theory (General Theory) f-04 Dimension of Metrizable Spaces f-05 Dimension Theory: Infinite Dimension f-06 Zero-Dimensional Spaces f-07 Linearly Ordered and Generalized Ordered Spaces f-08 Unicoherence and Multicoherence f-09 Topological Characterizations of Separable Metrizable Zero-Dimensional Spaces f-10 Topological Characterizations of Spaces f-11 Higher-Dimensional Local ConnectednessG Special spaces g-01 Extremally Disconnected Spaces g-02 Scattered Spaces g-03 Dowker SpacesH Connections with other structures h-01 Topological Groups h-02 TopologicalRings, Division Rings, Fields and Lattices h-03 Free Topological Groups h-04 Homogeneous Spaces h-05 Transformation Groups and Semigroups h-06 Topological Discrete Dynamical Systems h-07 Fixed Point Theorems h-08 Topological Representations of Algebraic SystemsJ Influencies of other fields j-01 Descriptive Set Theory j-02 Consistency Results in Topology, I: Quotable Principles 03 Consistency Results in Topology, II: Forcing and Large Cardinals j-04 Digital Topology j-05 Computer Science and Topology j-06 Non Standard Topology j-07 Topological Games j-08 Fuzzy Topological SpacesK Connections with other fields k-01 Banach Spaces and Topology (I) k-02 Banach Spaces (and Topology) (II) k-03 Measure Theory, I k-04 Measure Theory, II k-05 Polyhedra and Complexes k-06 Homology k-07 Homotopy, I k-08 Homotopy, II k-09 Shape Theory k-10 Manifold k-11 Infinite-Dimensional TopologySubject index

Reviews

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