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008			140112s1993 ne | s |||| 0|eng d
020			_a9789401581493 _9978-94-015-8149-3
082			_a514 _223
100			_aBeer, Gerald. _920290
245			_aTopologies on Closed and Closed Convex Sets _h[electronic resource] / _cby Gerald Beer.
250			_a1st ed. 1993.
260			_aDordrecht : _bSpringer Netherlands : _bImprint: Springer, _c1993.
300			_aXII, 340 p. _bonline resource.
520			_aThis 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.
650			_aTopology. _920291
650			_aFunctional analysis. _920292
650			_aMathematical optimization. _920293
650			_aTopology. _920291
650			_aFunctional Analysis. _920294
650			_aOptimization. _920295
856			_uhttps://doi.org/10.1007/978-94-015-8149-3
942			_cEBK
999			_c13626 _d13626