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Bornological convergences |
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| Authors: | A Lechicki |
| Institution: | a Softlab, Zamdorfer Str. 120, 81677 Munich, Germany b University of Milano-Bicocca, Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy c Opole University, Instytut Matematyki i Informatyki, Oleska 48, 45-052 Opole, Poland |
| Abstract: | We study a family of convergences (actually pretopologies) in the hyperspace of a metric space that are generated by covers of the space. This family includes the Attouch-Wets, Fell, and Hausdorff metric topologies as well as the lower Vietoris topology. The unified approach leads to new developments and puts into perspective some classical results. |
| Keywords: | Convergences Hyperspaces Covers Bornologies Pretopology Hausdorff metric topology Uniform structure Totally bounded sets |
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