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

Hardcover | June 1, 1997

byR. Lowen

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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 concepts as a special case of the concept of approach spaces. This theory providesan answer to natural questions in the interplay between topological and metric spaces by introducing a uniquely well suited supercategory of TOP and MET. The book explains the richness of approach structures in great detail; it provides a comprehensive explanation of the categorical set-up, developsthe 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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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 concepts as a special case of the concept of approach spaces. This theory providesan answer to natural questions in the inter...

R. Lowen is at University of Antwerp.

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Format:HardcoverDimensions:264 pages, 9.21 × 6.14 × 0.75 inPublished:June 1, 1997Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198500300

ISBN - 13:9780198500308

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Table of Contents

SymbolsPreface1. Approach Spaces2. Topological Approach Spaces3. Metric Approach Spaces4. Uniform Approach Spaces5. Canonical Examples6. Approach Properties7. Completion8. CompactificationAppendix AAppendix BIndexBibliography

Editorial Reviews

`This book is a landmark in the history of general topology...The book is carefully written...The book deserves a place on the shelves of mathematicians, especially topologists, who are interested in fundamentals.'S.A.Naimpally, Mathematical Reviews