Metric Spaces

E. T. Copson

doi:10.1017/CBO9780511566141

Metric space topology, as the generalization to abstract spaces of the theory of sets of points on a line or in a plane, unifies many branches of classical analysis and is necessary introduction to functional analysis. Professor Copson's book, which is based on lectures given to third-year undergraduates at the University of St Andrews, provides a more leisurely treatment of metric spaces than is found in books on functional analysis, which are usually written at graduate student level. His presentation is aimed at the applications of the theory to classical algebra and analysis; in particular, the chapter on contraction mappings shows how it provides proof of many of the existence theorems in classical analysis.

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Metric Spaces

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - Introduction
pp 1-20

2 - Metric Spaces
pp 21-30

3 - Open and Closed Sets
pp 31-45

4 - Complete Metric Spaces
pp 46-61

5 - Connected Sets
pp 62-71

6 - Compactness
pp 72-84

7 - Functions and Mappings
pp 85-110

8 - Some Applications
pp 111-136

9 - Further Developments
pp 137-142

Index
pp 143-143

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Metric Spaces

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