## Set-Valued Analysis"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." —Mathematical Reviews "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." —Zentralblatt Math |

### From inside the book

Results 1-5 of 89

Despite the emergence of exciting new vistas for the applications of mathematics, our long familiarity with sequences (of

**elements**) and with (single-valued) maps has perhaps been so deeply rooted in traditional mathematical ...

Studying limits of sets together with limits of

**elements**may have been very natural in this context. The topological ideas are, indeed, quite simple and straightforward. In the same way that topological concepts are based on the notions ...

We begin the first section by extending concepts of limits and cluster points of sequences of

**elements**to sequences of sets. These set- valued analogues have been introduced by Painleve in 1902 under the names of upper and lower limits ...

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.) ...

A generalized sequence is a map u e M i-> € X An

**element**x € X is the limit of if, for every neighborhood V of x, ... and that a subset K C X is compact if and only if every generalized sequence of

**elements**of K has a cluster point.

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