On complete metrizability of the Hausdorff metric topology

Zsilinszky, László

doi:10.1090/proc/13366

On complete metrizability of the Hausdorff metric topology
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Proc. Amer. Math. Soc. 145 (2017), 2281-2289 Request permission

Abstract:

It is shown that there exists a nonseparable completely metrizable bounded metric space $(X,d)$ such that the hyperspace $CL(X)$ of the nonempty closed subsets of $X$ endowed with the Hausdorff metric $H_d$ is not completely metrizable.

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