Topological and uniform spaces

I.M. James0387964665, 9780387964669

This book is a substantially revised edition of the UTM book: ISBN 0 387 96466-5, which is rewritten with a view to making the book far more accessible for undergraduates, particularly in the UK and Ireland. It contains more detailed explanations and ex ercises, together with fully worked solutions to the essential problems and a new chapter on the historical aspects.

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Table of contents :
Cover……Page 1
Series……Page 2
Title page……Page 3
Date-line……Page 4
Contents……Page 5
Introduction……Page 7
CHAPTER 0 Preliminaries……Page 11
CHAPTER 1 Topological Spaces……Page 19
CHAPTER 2 Continuity……Page 35
CHAPTER 3 The Induced Topology and Its Dual……Page 51
CHAPTER 4 Open Functions and Closed Functions……Page 63
CHAPTER 5 Compact Spaces……Page 72
CHAPTER 6 Separation Conditions……Page 81
CHAPTER 7 Uniform Spaces……Page 95
CHAPTER 8 The Uniform Topology……Page 111
CHAPTER 9 Connectedness……Page 124
CHAPTER 10 Countability and Related Topics……Page 140
CHAPTER 11 Functional Separation Conditions……Page 150
CHAPTER 12 Completeness and Completion……Page 158
Select Bibliography……Page 168
Index……Page 169