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On complete metrizability of the Hausdorff metric topology


Author: László Zsilinszky
Journal: Proc. Amer. Math. Soc. 145 (2017), 2281-2289
MSC (2010): Primary 54B20; Secondary 54E50, 54E52, 91A44
DOI: https://doi.org/10.1090/proc/13366
Published electronically: November 18, 2016
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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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László Zsilinszky
Affiliation: Department of Mathematics and Computer Science, The University of North Carolina at Pembroke, Pembroke, North Carolina 28372
Email: laszlo@uncp.edu

DOI: https://doi.org/10.1090/proc/13366
Keywords: Hausdorff distance, hyperspace, complete metrizability, strong Choquet game, Banach-Mazur game
Received by editor(s): March 4, 2014
Received by editor(s) in revised form: July 11, 2016
Published electronically: November 18, 2016
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society