Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad

Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad

by Robert Lowen
     
 

ISBN-10: 0198500300

ISBN-13: 9780198500308

Pub. Date: 06/28/1997

Publisher: Oxford University Press

In topology the three basic concepts of metrics, topologies and uniformities have been treated so far as separate entities by means of different methods and terminology. This is the first book to treat all three as a special case of the concept of approach spaces. This theory provides an answer to natural questions in the interplay between topological and metric

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Overview

In topology the three basic concepts of metrics, topologies and uniformities have been treated so far as separate entities by means of different methods and terminology. This is the first book to treat all three as a special case of the concept of approach spaces. This theory provides an answer to natural questions in the interplay between topological and metric spaces by introducing a uniquely well suited supercategory of TOP and MET. The theory makes it possible to equip initial structures of metricizable topological spaces with a canonical structure, preserving the numerical information of the metrics. It provides a solid basis for approximation theory, turning ad hoc notions into canonical concepts, and it unifies topological and metric notions. The book explains the richness of approach structures in great detail; it provides a comprehensive explanation of the categorical set-up, develops the basic theory and provides many examples, displaying links with various areas of mathematics such as approximation theory, probability theory, analysis and hyperspace theory.

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Product Details

ISBN-13:
9780198500308
Publisher:
Oxford University Press
Publication date:
06/28/1997
Series:
Oxford Mathematical Monographs Series
Pages:
262
Product dimensions:
6.30(w) x 9.20(h) x 0.80(d)

Table of Contents

Symbols
Preface
1. Approach Spaces
2. Topological Approach Spaces
3. Metric Approach Spaces
4. Uniform Approach Spaces
5. Canonical Examples
6. Approach Properties
7. Completion
8. Compactification
Appendix A
Appendix B
Index
Bibliography

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