Polishness of the Wijsman topology revisited
HTML articles powered by AMS MathViewer
- by László Zsilinszky PDF
- Proc. Amer. Math. Soc. 126 (1998), 3763-3765 Request permission
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
- Gerald Beer, A Polish topology for the closed subsets of a Polish space, Proc. Amer. Math. Soc. 113 (1991), no. 4, 1123–1133. MR 1065940, DOI 10.1090/S0002-9939-1991-1065940-6
- Gerald Beer, Topologies on closed and closed convex sets, Mathematics and its Applications, vol. 268, Kluwer Academic Publishers Group, Dordrecht, 1993. MR 1269778, DOI 10.1007/978-94-015-8149-3
- C. Costantini, Every Wijsman topology relative to a Polish space is Polish, Proc. Amer. Math. Soc. 123 (1995), no. 8, 2569–2574. MR 1273484, DOI 10.1090/S0002-9939-1995-1273484-5
- C.Costantini, On the hyperspace of a non-separable metric space, Proc. Amer. Math. Soc., to appear.
- Gustave Choquet, Lectures on analysis. Vol. I: Integration and topological vector spaces, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Edited by J. Marsden, T. Lance and S. Gelbart. MR 0250011
- C. Costantini, S. Levi, and J. Ziemińska, Metrics that generate the same hyperspace convergence, Set-Valued Anal. 1 (1993), no. 2, 141–157. MR 1239401, DOI 10.1007/BF01027689
- G. Debs, Espaces héréditairement de Baire, Fund. Math. 129 (1988), no. 3, 199–206 (French, with English summary). MR 962541, DOI 10.4064/fm-129-3-199-206
- Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597, DOI 10.1007/978-1-4612-4190-4
- A. Lechicki and S. Levi, Wijsman convergence in the hyperspace of a metric space, Boll. Un. Mat. Ital. B (7) 1 (1987), no. 2, 439–451 (English, with Italian summary). MR 896334
- László Zsilinszky, Baire spaces and hyperspace topologies, Proc. Amer. Math. Soc. 124 (1996), no. 8, 2575–2584. MR 1343733, DOI 10.1090/S0002-9939-96-03528-9
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
- MR Author ID: 331579
- Email: zsilinsz@math.sc.edu, laszlo@nat.uncp.edu
- Received by editor(s): January 20, 1997
- Received by editor(s) in revised form: April 28, 1997
- Communicated by: Alan Dow
- © Copyright 1998 American Mathematical Society
- 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