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
DOI:
https://doi.org/10.1090/S0002-9939-98-04956-9
MathSciNet review:
1618729
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Abstract | References | Similar Articles | Additional Information
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:
https://doi.org/10.1090/S0002-9939-98-04956-9
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