|
Polishness of the Wijsman topology revisited
Author(s):
László
Zsilinszky
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3763-3765.
MSC (1991):
Primary 54B20
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Let  be a completely metrizable space. Then the space of nonempty closed subsets of  endowed with the Wijsman topology is  -favorable in the strong Choquet game. As a consequence, a short proof of the Beer-Costantini Theorem on Polishness of the Wijsman topology is given.
References:
- [Be1]
- G.Beer, A Polish topology for the closed subsets of a Polish space, Proc. Amer. Math. Soc. 113 (1991), 1123-1133. MR 92c:54009
- [Be2]
- G.Beer, Topologies on Closed and Closed Convex Sets, Kluwer, Dordrecht, 1993. MR 95k:49001
- [Co1]
- C.Costantini, Every Wijsman topology relative to a Polish space is Polish, Proc. Amer. Math. Soc. 123 (1995), 2569-2574. MR 95j:54012
- [Co2]
- C.Costantini, On the hyperspace of a non-separable metric space, Proc. Amer. Math. Soc., to appear.
- [Ch]
- G.Choquet, Lectures on Analysis I., Benjamin, New York, 1969. MR 40:3252
- [CLZ]
- C.Costantini-S.Levi-J.Zieminska, Metrics that generate the same hyperspace convergence, Set-Valued Analysis 1 (1993), 141-157. MR 94h:54010
- [De]
- G.Debs, Espaces héréditairement de Baire, Fund. Math. 129 (1988), 199-206. MR 90a:54082
- [Ke]
- A.S.Kechris, Classical Descriptive Set Theory, Springer, New York, 1995. MR 96e:03057
- [LL]
- A.Lechicki-S.Levi, Wijsman convergence in the hyperspace of a metric space, Boll. Un. Mat. Ital. (7) B.1 (1987), 439-451. MR 88e:54007
- [Zs]
- L.Zsilinszky, Baire spaces and hyperspace topologies, Proc. Amer. Math. Soc. 124 (1996), 2575-2584. MR 96j:54017
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
54B20
Retrieve articles in all Journals with MSC
(1991):
54B20
Additional Information:
László
Zsilinszky
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Address at time of publication:
Department of Mathematics and Computer Science, University of North Carolina at Pembroke, Pembroke, North Carolina 28372
Email:
zsilinsz@math.sc.edu, laszlo@nat.uncp.edu
DOI:
10.1090/S0002-9939-98-04526-2
PII:
S 0002-9939(98)04526-2
Keywords:
Wijsman topology,
strong Choquet game,
strong Choquet space,
Polish space
Received by editor(s):
January 20, 1997
Received by editor(s) in revised form:
April 28, 1997
Communicated by:
Alan Dow
Copyright of article:
Copyright
1998,
American Mathematical Society
|
Comments: webmaster@ams.org