Selectors

John E. Jayne, C. Ambrose-Rogers

182 pages, parution le 09/12/2002

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Résumé

Though the search for good selectors dates back to the early twentieth century, selectors play an increasingly important role in current research. This book is the first to assemble the scattered literature into a coherent and elegant presentation of what is known and proven about selectors--and what remains to be found.

The authors focus on selection theorems that are related to the axiom of choice, particularly selectors of small Borel or Baire classes. After examining some of the relevant work of Michael and Kuratowski & Ryll-Nardzewski and presenting background material, the text constructs selectors obtained as limits of functions that are constant on the sets of certain partitions of metric spaces. These include selection theorems for maximal monotone maps, for the subdifferential of a continuous convex function, and for some geometrically defined maps, namely attainment and nearest-point maps.

Assuming only a basic background in analysis and topology, this book is ideal for graduate students and researchers who wish to expand their general knowledge of selectors, as well as for those who seek the latest results.

Contents

Chapter 1. Classical results

Michael's Continuous Selection Theorem
Results of Kuratowski and Ryll-Nardzewski
Remarks

Chapter 2. Functions that are constant on the sets of a disjoint discretely o-decomposable family of Fs-sets

Discretely o-Decomposable Partitions of a Metric Space
Functions of the First Borel and Baire Classes
When is a Function of the First Borel Class also of the First Baire Class?
Remarks

Chapter 3. Selectors for upper semi-continuous functions with non-empty compact values

A General Theorem
Special Theorems
Minimal Upper Semi-continuous Set-valued Maps
Remarks

Chapter 4. Selectors for compact sets

A Special Theorem
A General Theorem
Remarks

Chapter 5. Applications

Monotone Maps and Maximal Monotone Maps
Subdifferential Maps
Attainment Maps from X* to X
Attainment Maps from X to X*
Metric Projections or Nearest Point Maps
Some Selections into Families of Convex Sets
Example
Remarks

Chapter 6. Selectors for upper semi-continuous set-valued maps with nonempty values that are otherwise arbitrary

Diagonal Lemmas
Selection Theorems
A Selection Theorem for Lower Semi-continuous Set-valued Maps
Example
Remarks

Chapter 7. Further applications

Boundary Lemmas
Duals of Asplund Spaces
A Partial Converse to Theorem 5.4
Remarks

L'auteur - John E. Jayne

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

L'auteur - C. Ambrose-Rogers

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.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	John E. Jayne, C. Ambrose-Rogers
Parution	09/12/2002
Nb. de pages	182
Format	16 x 24
Couverture	Relié
Poids	472g
Intérieur	Noir et Blanc
EAN13	9780691096285
ISBN13	978-0-691-09628-5