Encyclopedia of General Topology (Hardcover)

Preface

Contributors

A 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 Spaces

C 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 Spaces

D Fairly general properties

d-01 The Low Separation Axioms T0 and T1

d-02 Higher Separation Axioms

d-03 Frechet 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 Lindelof 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 Constructions

E 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 Spaces

F 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 Connectedness

G Special spaces

g-01 Extremally Disconnected Spaces

g-02 Scattered Spaces

g-03 Dowker Spaces

H 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 Systems

J 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 Spaces

K 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 Topology

Subject index