On complete metrizability of the Hausdorff metric topology

Proc. Amer. Math. Soc. 145 (2017), 2281-2289 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, $\b...

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Bibliographic Details
Main Author Zsilinszky, Laszlo
Format Journal Article
LanguageEnglish
Published 15.03.2015
Subjects
Mathematics - General Topology
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Summary:Proc. Amer. Math. Soc. 145 (2017), 2281-2289 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.
DOI:10.48550/arxiv.1503.04383