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Introduction to Uniform Spaces

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This book can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, many of which are published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces.

Author(s): I. M. James
Series: London Mathematical Society Lecture Note Series
Publisher: Cambridge University Press
Year: 1990

Language: English
Pages: 153

Contents......Page 3
Introduction......Page 4
1. Uniform structures......Page 6
2. Induced and coinduced uniform structures......Page 21
3. The uniform topology......Page 34
4. Completeness and completion......Page 55
5. Topological groups......Page 75
6. Uniform transformation groups......Page 94
7. Uniform spaces over a base......Page 103
8. Uniform covering spaces......Page 116
Appendix: filters......Page 127
Exercises......Page 135
Bibliography......Page 142
Index......Page 144