**Mathematical Surveys and Monographs**

Volume: 12;
1964;
175 pp;
Softcover

MSC: Primary 54;

Print ISBN: 978-0-8218-1512-0

Product Code: SURV/12

List Price: $46.00

AMS Member Price: $36.80

MAA member Price: $41.40

**Electronic ISBN: 978-1-4704-1240-1
Product Code: SURV/12.E**

List Price: $46.00

AMS Member Price: $36.80

MAA member Price: $41.40

# Uniform Spaces

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*J. R. Isbell*

Uniform spaces play the same role for uniform continuity as
topological spaces for continuity. The theory was created in 1936 by A. Weil,
whose original axiomatization was soon followed by those of Bourbaki and Tukey;
in this book use is made chiefly of Tukey's system, based on uniform
coverings.

The organization of the book as a whole depends on the
Eilenberg-Mac Lane notions of category, functor and naturality, in the
spirit of Klein's Erlanger Program but with greater reach. The preface gives a
concise history of the subject since 1936 and a foreword outlines the category
theory of Eilenberg and Mac Lane. The chapters cover fundamental
concepts and constructions; function spaces; mappings into polyhedra; dimension
(1) and (2); compactifications and locally fine spaces. Most of the chapters
are followed by exercises, occasional unsolved problems, and a major unsolved
problem; the famous outstanding problem of characterizing the Euclidean plane
is discussed in an appendix. There is a good index and a copious bibliography
intended not to itemize sources but to guide further reading.

#### Table of Contents

# Table of Contents

## Uniform Spaces

- TABLE OF CONTENTS ix10
- PREFACE v6 free
- FOREWORD xi12 free
- CHAPTER I. Fundamental concepts 116 free
- CHAPTER II. Fundamental constructions 1328
- CHAPTER III. Function spaces 3651
- CHAPTER IV. Mappings into polyhedra 5671
- CHAPTER V. Dimension (1) 7893
- CHAPTER VI. Compactifications 97112
- CHAPTER VII. Locally fine spaces 123138
- CHAPTER VIII. Dimension (2) 146161
- APPENDIX. Line and plane 159174
- BIBLIOGRAPHY 163178
- INDEX 173188