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 70
... Limits of Sets 16 1.1.1 Definitions 16 1.1.2 The Compactness Theorem 23 1.1.3 The Duality Theorem 24 1.1.4 Convex Hull of Limits ... Upper Hemicontinuous Maps 74 3 Existence and Stability of an Equilibrium 77 3.1 Ky.
... upper semicontinuous maps 358 9.3 Minimal Selection 360 9.4 The Steiner Selection 364 9.4.1 Steiner Points of Convex Compact Sets .... 365 9.4.2 The Intersection Lemma 369 9.4.3 Lipschitz Selections of ... Upper and Lower Limits xvii.
Jean-Pierre Aubin, Hélène Frankowska. List of Figures 1.1 Example of Upper and Lower Limits of Sets 18 1.2 Graph of a Set- Valued Map and of its Inverse ...... 35 1.3 Semicontinuous and Noncontinuous Maps 40 3.1 Example of Monotone and ...
... limit is defined2.) Studying limits of sets together with limits of elements may have been very natural in this ... upper limits of sequences of sets, which are, so to speak, "thick" limits and cluster points respectively: The lower limit ...
... upper semi- continuity. These issues were developed in the monographs of ... upper semicontinuity, introducing parasitic artifacts. For example, using such topologies ... limits and leave aside the examination of topologies on power sets ...