Springer Science & Business Media, Mar 2, 2009 - Science - 461 pages
"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student."
—The Journal of the Indian Institute of Science
"The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. It includes...results with many historical comments giving the reader a sound perspective to look at the subject...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis."
"I recommend this book as one to dig into with considerable pleasure when one already knows the subject...‘Set-Valued Analysis’ goes a long way toward providing a much needed basic resource on the subject."
—Bulletin of the American Mathematical Society
"This book provides a thorough introduction to multivalued or set-valued analysis...Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and set-valued maps...The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis."
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9 Selections and Parametrization 353 9.1 Case of lower semicontinuous maps 355 9.2 Case of upper semicontinuous maps 358 9.3 Minimal Selection 360 9.4 The Steiner Selection 364 9.4.1 Steiner Points of Convex Compact Sets .
List of Figures 1.1 Example of Upper and Lower Limits of Sets 18 1.2 Graph of a Set- Valued Map and of its Inverse ...... 35 1.3 Semicontinuous and Noncontinuous Maps 40 3.1 Example of Monotone and Maximal Monotone Maps .
The second, extending the "V e, 3 6 — definition," leads to the so-called upper semicontinuity of set-valued maps2. Kuratowski showed however that semicontinuous maps are generically continuous. Lower semicontinuous maps are closely ...
We also provide a useful technical lemma: Lemma 1.1.6 Let us consider a sequence of subsets Ln c Z of a metric space Z and a sequence of subsets Mn CY of a compact metric space Y. Let ip : Z x Y t-> R be an upper semicontinuous function ...
We begin with the upper semicontinuous set-valued maps: 1.4.1 Definitions In this section, X, Y, Z denote metric spaces. We describe the concepts of semicontinuous set- valued maps introduced by Bouligand, Kuratowski and Wilson in the ...