Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Polishness of the Wijsman topology revisited


Author: László Zsilinszky
Journal: Proc. Amer. Math. Soc. 126 (1998), 3763-3765
MSC (1991): Primary 54B20
DOI: https://doi.org/10.1090/S0002-9939-98-04526-2
MathSciNet review: 1458275
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $X$ be a completely metrizable space. Then the space of nonempty closed subsets of $X$ endowed with the Wijsman topology is $\alpha $-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 [Enhancements On Off] (What's this?)

  • [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: https://doi.org/10.1090/S0002-9939-98-04526-2
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
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society