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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the hyperspace of a non-separable
metric space


Author: Camillo Costantini
Journal: Proc. Amer. Math. Soc. 126 (1998), 3393-3396
MSC (1991): Primary 54B20; Secondary 54E35, 54D35
MathSciNet review: 1618729
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Abstract: We prove the following two results. 1) There exists a non-separable complete metric space whose Wijsman hypertopology is not Cech-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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04956-9
PII: S 0002-9939(98)04956-9
Keywords: Non-separable metric space, Wijsman hypertopology, \v{C}ech-complete\-ness, Borel sets
Received by editor(s): January 17, 1996
Received by editor(s) in revised form: November 18, 1996
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1998 American Mathematical Society