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 78
... sequences of singleta {xn}, the set limit, when it exists, is either empty (the sequence of elements xn is not converging), or is a singleton made of the limit of the sequence. It is easy to check that: Proposition 1.1.2 If (-Kn)neN *s a ...
... there exists v > u such that xu e V. We recall that a single-valued map / from a topological space X to another Y is continuous at x if it maps any generalized sequence converging to x to a generalized sequence converging to f(x) and ...
... sequence of elements xp € X converges weakly to x G X if and only if for any q e X*, < q, > converges to < q, x > and a sequence ... exists a countable basis spanning a dense vector space. The separability concept goes back to Prechet. We ...
... exists Ni such that Vn > JVi, Mn C WU V Therefore LnC\Mn <zU for all n > max(iVo, N\). □ Remark — If M is not ... sequence of subsets Ln c Z of a metric space Z and a sequence of subsets Mn CY of a compact metric space Y. Let ip : Z x Y ...
... exists an integer No such that Vn>iV0, Mn C [J N(yi) i=l,...,n Set JV ... sequence of subsets Kn of a separable metric space X contains a subsequence ... sequence of subsets Kn. We shall construct a sequence of subsequences (-ftTn"^)n>o ...