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Topologies on Closed and Closed Convex Sets

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Kurzbeschreibung

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.

Details
Schlagworte

Titel: Topologies on Closed and Closed Convex Sets
Autoren/Herausgeber: Gerald Beer
Aus der Reihe: Mathematics and Its Applications
Ausgabe: Softcover reprint of hardcover 1st ed. 1993

ISBN/EAN: 9789048143337

Seitenzahl: 340
Format: 23,5 x 15,5 cm
Produktform: Taschenbuch/Softcover
Gewicht: 545 g
Sprache: Englisch

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