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

ISBN-13: 9780198500308 / Angielski / Twarda / 1997 / 262 str.

Robert Lowen; R. Lowen

Opis

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.

Recenzje

This book gives a new and complete development of the fundamentals of the theory of approach spaces as originally introduced by the author between 1987 and 1989... an approach structure is the richest structure, overlying the initial topology, which one can preserve when making such initial structures.