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arXiv · 1503.04383

On complete metrizability of the Hausdorff metric topology

Laszlo Zsilinszky
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Abstract

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.

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Laszlo Zsilinszky. 2015-03-15. On complete metrizability of the Hausdorff metric topology. https://arxiv.org/abs/1503.04383

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