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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The topological ideas are, indeed, quite simple and straightforward. In the same way that topological concepts are based on the notions of limits and cluster points of sequences of elements, their set-valued analogues are rooted in the ...
For instance, when we regard a set-valued map as a single- valued map from one set to the power set of the other (supplied with any one of the topologies we can think of) , we arrive at continuity concepts which are stronger than both ...
His definitions have been canonized ever since: A function was allowed to be differentiated only if the differential quotients were converging to the derivative for the pointwise convergence topology. The need to use nondif- ferentiable ...
Chapter 1 Continuity of Set- Valued Maps Introduction This chapter is devoted to the elementary topological properties of sequences of sets and set-valued maps. We begin the first section by extending concepts of limits and cluster ...
We may need the above extension when dealing with weak topologies of a Banach space X and of its dual denoted by X*. ... We recall that the weakened topology cr(X, X*) of X is defined by the semi-norms Pm(x) := sup | < q,x > | qeM when ...