## 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 30

... sequence converging to x to a generalized sequence converging to f(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. (See for instance [148, Section 1.7].) ...

We introduce the (negative) polar cones to subsets

**K C X**and LcX* denned by K~ := {pe X* | Vx G <p,a:>< 0} and L~ := {i€l| VpeL, <p,x>< 0} Let it — Limsupjj^ooiiL" denote the sequentially weak upper limit of the polar cones K~ .

When F is proper, the images F(K) of closed subsets

**K C X**are closed and the inverse images F~1(M) of compact subsets M C Y are compact. Indeed, we can write r : X >-> R+ Fr(x) := F(x) n r{x)B i) F{K) = Try (Graph(f1) D(KxY)) In ...

... we obtain the following consequence: Corollary 2.2.5 Let us consider Banach spaces X, Y , a continuous linear operator A 6 C{X, Y) and a closed convex cone

**K C X**such that A(K) — Y . Then the set-valued map y A~l{y) n K is ...

The subsets are called respectively the bipolar set and bipolar cone of a subset

**K C X**and the subspace K±A- := (.K'"L)"L C X the biorthogonal of It is clear that if° is a closed convex subset containing 0, that -K"- is a closed convex ...

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