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On the hyperspace of a non-separable metric space
Author(s):
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.
References:
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- G. Beer, A Polish topology for the closed subsets of a Polish space, Proc. Amer. Math. Soc. 113 (1991), 1123-1133. MR 92c:54009
- [CLZ]
- C. Costantini, S. Levi and J. Zieminska, Metrics that generate the same hyperspace convergence, Set-Valued Anal. 1 (1993), 141-157. MR 94h:54010
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- C. Costantini, Every Wijsman topology relative to a Polish space is Polish, Proc. Amer. Math. Soc. 123 (1995), 2569-2574. MR 95j:54012
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- R. Engelking, General Topology, revised and completed edition, Heldermann Verlag, Berlin, 1989. MR 91c:54001
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- C. Hess, Loi de la probabilité et indépendence des ensembles aléatoires à valeurs fermées dans un espace de Banach, Séminaire d'Analyse Convexe de l'Université de Montpellier, Exposé 7, 1983. MR 85m:60020
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- A. S. Kechris, Classical Descriptive Set Theory, Springer-Verlag, New York, 1995. MR 96e:03057
- [Zs]
- L. Zsilinszky, Baire spaces and hyperspace topologies, Proc. Amer. Math. Soc. 124 (1996), 2575-2584. MR 96j:54017
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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:
10.1090/S0002-9939-98-04956-9
PII:
S 0002-9939(98)04956-9
Keywords:
Non-separable metric space,
Wijsman hypertopology,
\v{C}ech-completeness,
Borel sets
Received by editor(s):
January 17, 1996
Received by editor(s) in revised form:
November 18, 1996
Communicated by:
Franklin D. Tall
Copyright of article:
Copyright
1998,
American Mathematical Society
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