Jayne / Rogers Selectors

Course Book
ISBN: 978-1-4008-2512-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 184 Seiten

John E. Jayne, PhD, DSc, is Professor of Mathematics at University College London and has been President of the International Mathematics Competition for university students since its inception in 1994. C. Ambrose Rogers, DSc, FRS, is Professor Emeritus at University College London, where he was Astor Professor of Mathematics for almost thirty years. He is an Elected Fellow of the Royal Society and a former President of the London Mathematical Society. His many awards and honors include the Junior Berwick Prize and De Morgan Medal of the London Mathematical Society.

Autoren/Hrsg.

Jayne, John E.

Rogers, C. Ambrose

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

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

Über Autor(innen)

John E. Jayne, PhD, DSc, is Professor of Mathematics at University College London and has been President of the International Mathematics Competition for university students since its inception in 1994. C. Ambrose Rogers, DSc, FRS, is Professor Emeritus at University College London, where he was Astor Professor of Mathematics for almost thirty years. He is an Elected Fellow of the Royal Society and a former President of the London Mathematical Society. His many awards and honors include the Junior Berwick Prize and De Morgan Medal of the London Mathematical Society.