On complete metrizability of the Hausdorff metric topology

There exists a completely metrizable bounded metrizable space \(X\) with compatible metrics \(d,d'\) so that the hyperspace \(CL(X)\) of nonempty closed subsets of \(X\) endowed with the Hausdorff metric \(H_d\), \(H_{d'}\), resp. is \(\alpha\)-favorable, \(\beta\)-favorable, resp. in the...

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Bibliographic Details
Published inarXiv.org
Main Author Zsilinszky, Laszlo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.03.2015
Subjects
Hyperspaces
Metric space
Topology
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Summary:There exists a completely metrizable bounded metrizable space \(X\) with compatible metrics \(d,d'\) so that the hyperspace \(CL(X)\) of nonempty closed subsets of \(X\) endowed with the Hausdorff metric \(H_d\), \(H_{d'}\), resp. is \(\alpha\)-favorable, \(\beta\)-favorable, resp. in the strong Choquet game. In particular, there exists a completely metrizable bounded metric space \((X,d)\) such that \((CL(X),H_d)\) is not completely metrizable.
ISSN:2331-8422