Proximity Spaces

Abstract

This tract provides a compact introduction to the theory of proximity spaces and their generalisations, making the subject accessible to readers having a basic knowledge of topological and uniform spaces, such as can be found in standard textbooks. Two chapters are devoted to fundamentals, the main result being the proof of the existence of the Smirnov compactification using clusters. Chapter 3 discusses the interrelationships between proximity spaces and uniform spaces and contains some of the most interesting results in the theory of proximity spaces. The final chapter introduces the reader to several generalised forms of proximity structures and studies one of them in detail. The bibliography contains over 130 references to the scattered research literature on proximity spaces, in addition to general references.