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Selectors by John E. Jayne (English) Hardcover Book
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Item specifics
- Condition
- Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab
- ISBN-13
- 9780691096285
- Book Title
- Selectors
- ISBN
- 9780691096285
About this product
Product Identifiers
Publisher
Princeton University Press
ISBN-10
0691096287
ISBN-13
9780691096285
eBay Product ID (ePID)
2228856
Product Key Features
Number of Pages
184 Pages
Publication Name
Selectors
Language
English
Subject
Numerical Analysis, General, Topology
Publication Year
2002
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
0.8 in
Item Weight
14 Oz
Item Length
9.5 in
Item Width
7.9 in
Additional Product Features
Intended Audience
College Audience
LCCN
2002-108315
Dewey Edition
21
Dewey Decimal
511.3/22
Table Of Content
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 F s -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
Synopsis
Focuses on selection theorems that are related to the axiom of choice, particularly selectors of small Borel or Baire classes. This text constructs selectors obtained as limits of functions that are constant on the sets of certain partitions of metric spaces. It is aimed at students and researchers who wish to expand their knowledge of selectors., Though the search for good selectors dates back to the early 20th century, selectors play an important role in contemporary research. This book assembles the literature into a 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 and 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 maximum monotone maps, for the subdifferential of a continous convex function, and for some geometrically defined maps, namely attainment and nearest-point maps., 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.
LC Classification Number
QA611.J39 2002
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- g***r (1266)- Feedback left by buyer.Past monthVerified purchaseGreat item. Fast shipping. Very pleased.
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Seller feedback (1,054,252)
- g***r (1266)- Feedback left by buyer.Past monthVerified purchaseGreat item. Fast shipping. Very pleased.
- o***s (570)- Feedback left by buyer.Past monthVerified purchaseGreat, book! Fast shipping and excellent packing. Fantastic seller, thanks!
- _***f (27)- Feedback left by buyer.Past monthVerified purchaseThe book arrived in pristine condition- brand new and wrapped in plastic. This book was priced very fairly. Delivery took a little longer than expected, but the seller was very responsive and transparent. Overall, this has been a great experience and I would buy from this seller again.