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."
Results 1-5 of 84
Contents Introduction 1 1 Continuity of Set- Valued Maps 15 1.1 Limits of Sets 16 1.1.1 Definitions 16 1.1.2 The Compactness Theorem 23 1.1.3 The Duality Theorem 24 1.1.4 Convex Hull of Limits 26 1.2 Calculus of Limits 27 1.2.1 Direct ...
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 ...
They have been popularized by Kuratowski in his famous book Topologie and thus, often called Kuratowski lower and upper limits of sequences of sets. Definition 1.1.1 Let (-Kn)neN be a sequence of subsets of a metric space X. We say that ...
Instead, for the sake of simplicity, we shall use the concept of sequentially weak upper limit: Definition 1.1.3 Let us consider a sequence of subsets Kn of the dual of a Banach space. We shall say that the subset a - Limsup^ooifn of ...
You have reached your viewing limit for this book.