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
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... vector-spaces, since set- valued analysis is also useful for solving problems involving partial differential equations or inclusions. But whenever the proofs of the finite-dimensional and infinite- dimensional statements are quite ...
... 4 . 5 Properties of Normal Cones In Finite Dimensional Vector Spaces 158 4.6 Properties of m^-order Contingent Sets 172 4.7 Properties of mt/l-order Adjacent Sets 174 Introduction It is a fact that in mathematical sciences there xix.
... vector subspaces is still too restrictive: We need to use the notion of closed convex cone, which is a kind of vector subspace in which it is forbidden to use subtraction. These cones enjoy many properties of the vector subspaces. For ...
... vectors must be a vector space, so that the original idea became concealed after its formal implementation in differential geometry. If we come back to the idea underlying the notion of tangency to a subset K at some point x € K, we are ...
... , that there exists a countable basis spanning a dense vector space. The separability concept goes back to Prechet. We also point out the quite impressive equivalent formulation of 20 Continuity of Set-Valued Maps 40441_20.pdf.