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


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 Generaliz


No. of pages:
© 2003
Elsevier Science
Print ISBN:
Electronic ISBN:

About the authors

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


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