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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In the same way that topological concepts are based on the notions of limits and cluster points of sequences of ... which are, so to speak, "thick" limits and cluster points respectively: The lower limit of a sequence of subsets Kn is ...
Convergence of Maps What about the convergence of a sequence of set- valued maps p ? ± n • The first idea which comes to mind is to extend the various notions of uniform convergence of single- valued maps, regarded as a map from one ...
We begin the first section by extending concepts of limits and cluster points of sequences of elements to sequences of sets. ... We shall call them simply lower and upper limits: The lower limit of a sequence of subsets Kn is the set of ...
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 ...
Any decreasing sequence of subsets Kn has a limit, which is the intersection of their closures: if Kn C Km when n > m, then Limn->oo^n — f") Kn n>0 An upper limit may be empty (no subsequence of elements xn G Kn has a cluster point.) ...