# Encyclopedia of General Topology

## 1st Edition

**Authors:**K.P. Hart Jun-iti Nagata J.E. Vaughan

**Hardcover ISBN:**9780444503558

**eBook ISBN:**9780080530864

**Imprint:**Elsevier Science

**Published Date:**18th November 2003

**Page Count:**536

## Description

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

## Readership

Working mathematicians and graduate students in mathematics. Mathematicians working in General Topology and related areas.

## Table of Contents

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 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 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

## Details

- No. of pages:
- 536

- Language:
- English

- Copyright:
- © Elsevier Science 2003

- Published:
- 18th November 2003

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9780080530864

- Hardcover ISBN:
- 9780444503558

## About the Author

### K.P. Hart

### Affiliations and Expertise

Delft University of Technology, Faculty of Information, Technology and Systems, The Netherlands

### Jun-iti Nagata

### Affiliations and Expertise

Uzumasa, Osaka, Japan

### J.E. Vaughan

### Affiliations and Expertise

University of North Carolina, Department of Mathematics, Greensboro, NC, USA

## Reviews

The book will be very useful for the mathematical community.

Ljubisa Kocinac (Aleksandrovac). Mathematical Reviews, 2005