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

Lowen, Robert

ISBN 10: 0198500300 / ISBN 13: 9780198500308

Published by Clarendon Press, 1997

About this Item

Seller Inventory # 1556745-n

Bibliographic Details

• Title: Approach Spaces : The Missing Link in the Topology-Uniformity-Metric Triad
• Publisher: Clarendon Press
• Publication Date: 1997
• Language: English
• ISBN 10: 0198500300
• ISBN 13: 9780198500308
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

About the Author

R. Lowen is at University of Antwerp.