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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Amsterdam properties of Wijsman hyperspaces
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by Jiling Cao and Heikki J. K. Junnila PDF
Proc. Amer. Math. Soc. 138 (2010), 769-776 Request permission


In this paper we show the following results: (i) there exists a separable metric space of the first category whose Wijsman hyperspace is almost countably subcompact; (ii) there exists a $\sigma$-discrete crowded metric space whose Wijsman hyperspace is countably base-compact. Neither of these can occur with Vietoris hyperspaces.
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Additional Information
  • Jiling Cao
  • Affiliation: School of Computing and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand
  • Email:
  • Heikki J. K. Junnila
  • Affiliation: Department of Mathematics and Statistics, The University of Helsinki, P. O. Box 68, FI-00014, Helsinki, Finland
  • Email:
  • Received by editor(s): February 3, 2009
  • Received by editor(s) in revised form: June 8, 2009
  • Published electronically: September 9, 2009
  • Additional Notes: Research for this paper was partially conducted during the first author’s visit to the University of Helsinki in July 2008. He would like to acknowledge financial support from the Magnus Ehrnrooth Foundation, administered by the Finnish Society of Sciences and Letters, and he also thanks the Department of Mathematics and Statistics for hospitability.
    The second author’s research was partially supported by Natural Science Foundation of China grant 10671173.
  • Communicated by: Alexander Dranishnikov
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 769-776
  • MSC (2000): Primary 54E52; Secondary 54B10, 54B20
  • DOI:
  • MathSciNet review: 2557194