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 48
... Set - Valued Maps Continuity of Set - Valued maps Definitions 1.4.2 Generic Continuity 1.4.3 Example : Parametrized Set - Valued Maps 1.4.4 Marginal Maps · 1.5 Lower Semi - Continuity Criteria 2 Closed Convex Processes 2.2 Open Mapping ...
... set - valued maps are closed convex processes , which is a desirable property for a derivative3 . Indeed , the two basic theorems on continuous linear operators due to Banach , the Closed Graph Theorem ( equivalent to the Open Mapping ...
... subsets of X. { x1 , .. хм In other words , a generalized sequence of elements μ EX ... subset σ - Limsupn∞ Kn of weak- limits of subsequences of elements xn Є Kn ... open subsets , or , equivalently , that there exists a countable basis ...
... open neighborhood U , the subset K = M \ U is not empty , disjoint of Limsupn∞ Ln and is compact by assumption . : = Let y belong to K. Since y does not belong to Limsupno Ln , there exist εy > 0 and Ny such that , for all n > Ny , y ...
... subsets Kn of a separable metric space X contains a subsequence which has a ( pos- sibly empty ) limit . Proof- Since X is separable , there exists a countable family of open subsets Um satisfying the following property : Э V open subset ...