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

James, I. M.

Cambridge University Press（1990/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 160 p.
• 言語 ENG
• 商品コード 9780521386203
• DDC分類 514.3202

基本説明

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.

Full Description

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

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.