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. © 2004 Elsevier Inc. All rights reserved.
Lechicki, A., Levi, S., Spakowski, A. (2004). Bornological convergences. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 297(2), 751-770 [10.1016/j.jmaa.2004.04.046].
Bornological convergences
LEVI, SANDRO;
2004
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. © 2004 Elsevier Inc. All rights reserved.
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