Introduction to Uniform Spaces (London Mathematical Society Lecture Note Series, Series Number 144)

This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and 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, much of which is 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. Readers interested in general topology will find much to interest them here. 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

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.

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. Based on a course taught to an audience of undergraduate and graduate students at Oxford, this book can be viewed as a bridge between the study of metric spaces and general topological spaces.