Gerald Beer

(Author)

Topologies on Closed and Closed Convex SetsPaperback, 15 December 2010

Topologies on Closed and Closed Convex Sets
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Part of Series
Mathematics and Its Applications
Part of Series
Mathematics and Its Applications (Kluwer Academic)
Print Length
340 pages
Language
English
Publisher
Springer
Date Published
15 Dec 2010
ISBN-10
9048143330
ISBN-13
9789048143337

Description

This monograph provides an introduction to the theory of topologies defined on the closed subsets of a metric space, and on the closed convex subsets of a normed linear space as well. A unifying theme is the relationship between topology and set convergence on the one hand, and set functionals on the other. The text includes for the first time anywhere an exposition of three topologies that over the past ten years have become fundamental tools in optimization, one-sided analysis, convex analysis, and the theory of multifunctions: the Wijsman topology, the Attouch--Wets topology, and the slice topology. Particular attention is given to topologies on lower semicontinuous functions, especially lower semicontinuous convex functions, as associated with their epigraphs. The interplay between convex duality and topology is carefully considered and a chapter on set-valued functions is included. The book contains over 350 exercises and is suitable as a graduate text.
This book is of interest to those working in general topology, set-valued analysis, geometric functional analysis, optimization, convex analysis and mathematical economics.

Product Details

Author:
Gerald Beer
Book Format:
Paperback
Country of Origin:
NL
Date Published:
15 December 2010
Dimensions:
22.86 x 15.24 x 2.29 cm
ISBN-10:
9048143330
ISBN-13:
9789048143337
Language:
English
Location:
Dordrecht
Pages:
340
Publisher:
Weight:
476.27 gm

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