Introduction to Uniform Spaces [Paperback]

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.Introduction; 1. Uniform structures; 2. Induced and coinduced uniform structures; 3. The uniform topology; 4. Completeness and completion; 5. Topological groups; 6. Uniform transformation groups; 7. Uniform spaces over a base; 8. Uniform covering spaces; Exercises; Bibliography.