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Amsterdam properties of Wijsman hyperspaces

Authors: Jiling Cao and Heikki J. K. Junnila
Journal: Proc. Amer. Math. Soc. 138 (2010), 769-776
MSC (2000): Primary 54E52; Secondary 54B10, 54B20
Published electronically: September 9, 2009
MathSciNet review: 2557194
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Abstract: 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

Heikki J. K. Junnila
Affiliation: Department of Mathematics and Statistics, The University of Helsinki, P. O. Box 68, FI-00014, Helsinki, Finland

Keywords: Baire space, ball topology, pseudocomplete, subcompact, Wijsman topology.
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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