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OverviewThis 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. Full Product DetailsAuthor: Gerald BeerPublisher: Springer Imprint: Springer Edition: Softcover reprint of hardcover 1st ed. 1993 Volume: 268 Dimensions: Width: 15.50cm , Height: 1.80cm , Length: 23.50cm Weight: 0.545kg ISBN: 9789048143337ISBN 10: 9048143330 Pages: 340 Publication Date: 15 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPreface. 1. Preliminaries. 2. Weak Topologies determined by Distance Functionals. 3. The Attouch--Wets and Hausdorff Metric Topologies. 4. Gap and Excess Functionals and Weak Topologies. 5. The Fell Topology and Kuratowski--Painlevé Convergence. 6. Multifunctions - the Rudiments. 7. The Attouch--Wets Topology for Convex Functions. 8. The Slice Topology for Convex Functions. Notes and References. Bibliography. Symbols and Notation. Subject Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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