Springer Science & Business Media, Mar 2, 2009 - Science - 461 pages
"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."
"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."
Results 1-5 of 60
In view of such a wide variety of motivating applications, it is fortunate that most of the basic results of the chapters of "single- valued" analysis can be adapted to the set-valued realm. These include: • Limits and Continuity ...
... of Hadamard's tablets, existence, uniqueness and stability, we shall only retain the stability requirements, which can be encapsulated in adequate definitions of continuity of This is one of the topics of the first chapter. 2.
Jean-Pierre Aubin, Hélène Frankowska. Therefore, this limited class of set-valued maps is in essence made of families of single-valued maps. Chapter 1 Continuity of Set- Valued Maps Introduction This chapter Introduction 40441_14.pdf.
Chapter 1 Continuity of Set- Valued Maps Introduction This chapter is devoted to the elementary topological properties of sequences of sets and set-valued maps. We begin the first section by extending concepts of limits and cluster ...
The definitions introduced in this chapter are basic and will be used throughout the book. 1.1 Limits of Sets 1.1.1 Definitions Let X be a metric space supplied with a distance d. When K is a subset of X, we denote by dx(x) := d(x,K) ...