Topologies on Closed and Closed Convex Sets [electronic resource] / by Gerald Beer.
Material type: Computer filePublication details: Dordrecht : Springer Netherlands : Imprint: Springer, 1993.Edition: 1st ed. 1993Description: XII, 340 p. online resourceISBN:- 9789401581493
- 514Â 23
Item type | Home library | Call number | Status | Date due | Barcode | Item holds | |
---|---|---|---|---|---|---|---|
e-Book | S. R. Ranganathan Learning Hub Online | 514 (Browse shelf(Opens below)) | Available | EB1494 |
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512.943 4 Z28M Matrix Analysis and Applications | 512.9434 H78M Matrix Analysis | 513.83 W661G General Topology | 514 Topologies on Closed and Closed Convex Sets | 514 P435F Foundations of General Topology | 514.09 R398E Euler's Gem : The Polyhedron Formula and the Birth of Topology | 514.2 Fundamentals of Differential Geometry |
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.
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