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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On complete metrizability of the Hausdorff metric topology
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by László Zsilinszky PDF
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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Additional Information
  • László Zsilinszky
  • Affiliation: Department of Mathematics and Computer Science, The University of North Carolina at Pembroke, Pembroke, North Carolina 28372
  • MR Author ID: 331579
  • Email: laszlo@uncp.edu
  • 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
  • © Copyright 2016 American Mathematical Society
  • 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
  • MathSciNet review: 3611337