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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 the hyperspace of a non-separable metric space
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by Camillo Costantini PDF
Proc. Amer. Math. Soc. 126 (1998), 3393-3396 Request permission

Abstract:

We prove the following two results. 1) There exists a non-separable complete metric space whose Wijsman hypertopology is not Čech-complete. 2) There exist a non-separable metrizable space and two compatible metrics on it, such that the collections of the Borel sets generated by the relative Wijsman hypertopologies do not coincide.
References
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Additional Information
  • Camillo Costantini
  • Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
  • Email: costantini@dm.unito.it
  • Received by editor(s): January 17, 1996
  • Received by editor(s) in revised form: November 18, 1996
  • Communicated by: Franklin D. Tall
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3393-3396
  • MSC (1991): Primary 54B20; Secondary 54E35, 54D35
  • DOI: https://doi.org/10.1090/S0002-9939-98-04956-9
  • MathSciNet review: 1618729