Topological Spaces
About This Book
Topological Spaces focuses on the applications of the theory of topological spaces to the different branches of mathematics. The book first offers information on elementary principles, topological spaces, and compactness and connectedness. Discussions focus on locally compact spaces, local connectedness, fundamental concepts and their reformulations, lattice of topologies, axioms of separation, fundamental concepts of set theory, and ordered sets and lattices. The manuscript then ponders on mappings and extensions and characterization of topological spaces, including completely regular spaces, transference of topologies, Wallman compactification, and embeddings. The publication takes a look at metric and uniform spaces and applications of topological groups. Topics include the Stone-Weierstrass Approximation Theorem, extensions and completions of topological groups, topological rings and fields, extension and completion of uniform spaces, uniform continuity and uniform convergence, metric spaces, and metritization. The text is a valuable reference for mathematicians and researchers interested in the study of topological spaces.
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Table of contents
- Front Cover
- Topological Spaces
- Copyright Page
- Table of Contents
- PREFACE
- Introduction
- Chapter I. Elementary Principles
- Chapter II. Topological Spaces
- Chapter Ill. Compactness and Connectedness
- Chapter IV. Mappings
- Chapter V. Extensions and Characterization of Topological Spaces
- Chapter VI. Metric and Uniform Spaces
- Chapter VII. Topological Groups. Applications
- NOTATIONS EMPLOYED
- BIBLIOGRAPHY
- Subject Index