Approach Spaces

The Missing Link in the Topology-Uniformity-Metric Triad

By: R. Lowen

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Hardcover | 26 June 1997

At a Glance

Hardcover
264 Pages

Dimensions(cm)
22.86 x 15.24 x 1.91

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$134.15

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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 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.

Industry 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

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