Introduction to Uniform Spaces

✍ Scribed by I. M. James

• Publisher: Cambridge University Press
• Year: 1990
• Tongue: English
• Leaves: 153
• Series: London Mathematical Society Lecture Note Series
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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