TABLE OF CONTENTS: Preface vii
Introduction ix
Chapter 1. Classical results 1
1.1 Michael's Continuous Selection Theorem 1
1.2 Results of Kuratowski and Ryll-Nardzewski 8
1.3 Remarks 13
Chapter 2. Functions that are constant on the sets of a disjoint discretely o-decomposable family of Fs-sets 19
2.1 Discretely o-Decomposable Partitions of a Metric Space 19
2.2 Functions of the First Borel and Baire Classes 25
2.3 When is a Function of the First Borel Class also of the First Baire Class? 39
2.4 Remarks 42
Chapter 3. Selectors for upper semi-continuous functions with non-empty compact values 43
3.1 A General Theorem 45
3.2 Special Theorems 53
3.3 Minimal Upper Semi-continuous Set-valued Maps 53
3.4 Remarks 57
Chapter 4. Selectors for compact sets 65
4.1 A Special Theorem 67
4.2 A General Theorem 69
4.3 Remarks 88
Chapter 5. Applications 91
5.1 Monotone Maps and Maximal Monotone Maps 95
5.2 Subdifferential Maps 101
5.3 Attainment Maps from X* to X 106
5.4 Attainment Maps from X to X* 107
5.5 Metric Projections or Nearest Point Maps 108
5.6 Some Selections into Families of Convex Sets 110
5.7 Example 118
5.8 Remarks 122
Chapter 6. Selectors for upper semi-continuous set-valued maps with nonempty values that are otherwise arbitrary 123
6.1 Diagonal Lemmas 124
6.2 Selection Theorems 127
6.3 A Selection Theorem for Lower Semi-continuous Set-valued Maps 138
6.4 Example 140
6.5 Remarks 144
Chapter 7. Further applications 147
7.1 Boundary Lemmas 149
7.2 Duals of Asplund Spaces 151
7.3 A Partial Converse to Theorem 5.4 156
7.4 Remarks 159
Bibliography 161
Index 165
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