TABLE OF CONTENTS
PREFACE v
FOREWORD xi
Categories xi
CHAPTER
I. Fundamental concepts 1
Metric uniform spaces 1
Uniformities and preuniformities 3
Uniform topology and uniform continuity 6
Exercises 1]
Notes 12
CHAPTER
II. Fundamental constructions 13
Sum, product, subspace, quotient 13
Completeness and completion 17
Compactness and compactification 20
Proximity 24
Hyperspace 27
Exercises 32
Notes 35
CHAPTER
III. Function spaces 36
The functor U 36
Injective spaces 39
Equiuniform continuity and semi-uniform products 43
Closure properties \ . . . 49
Exercises 52
Research Problem A 54
Research Problem Bx 54
Notes 55
CHAPTER
IV. Mappings into polyhedra 56
Uniform complexes 56
Canonical mappings 61
Extensions and modifications 65
Inverse limits 70
Exercises 73
Research Problem B2 76
Notes 76
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