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| Volume 4, Number 3, September 2008, pp. 393-409 | |||||||||
| Gerald Beer | |||||||||
| Key words: | |||||||||
| Attouch-Wets convergence, bounded Hausdorff convergence, bornological convergence, convex function, Fenchel conjugate | |||||||||
| Mathematices Subject Classification: 54B20; 46A55, 26A51 | |||||||||
|
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| Volume 4, Number 3, September 2008, pp. 393-409 | |||||||||
| Gerald Beer | |||||||||
| Key words: | |||||||||
| Attouch-Wets convergence, bounded Hausdorff convergence, bornological convergence, convex function, Fenchel conjugate | |||||||||
| Mathematices Subject Classification: 54B20; 46A55, 26A51 | |||||||||
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| Abstract: | |||
| We survey the basic facts about Attouch-Wets convergence, also called bounded Hausdorff convergence, and the associated Attouch-Wets topology for the nonempty closed subsets of a metric space as well as for the proper lower semicontinuous convex functions defined on a normed linear linear space X as identified with their convex epigraphs in X × lR. Some new results and simpler proofs of old results are included. With our emphasis on topological results, this article complements [58]. | |||
| The Attouch-Wets topology in metric and normed spaces | ||