Topologies on Closed and Closed Convex Sets

By:

Gerald Beer

Format:

Paperback / softback

Series:

Mathematics and its Applications

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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.

Release date Australia

December 15th, 2010

Author

Gerald Beer

Audience

Professional & Vocational

Edition

Softcover reprint of hardcover 1st ed. 1993

Illustrations

XII, 340 p.

Pages

340

Series

Mathematics and its Applications

Dimensions

155x235x18

ISBN-13

9789048143337

Product ID

8940342

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