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 concepts 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 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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9780198500308

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`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

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. L Enseignement Mathematique

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