Every Wijsman topology relative to a Polish space is Polish
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- by C. Costantini
- Proc. Amer. Math. Soc. 123 (1995), 2569-2574
- DOI: https://doi.org/10.1090/S0002-9939-1995-1273484-5
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Abstract:
Generalizing a result of G. Beer and a result of E. Effros, we show that if (X, d) is a separable and completely metrizable metric space, then the hyperspace of X endowed with the Wijsman topology is separable and completely metrizable.References
- A. Barbati, Strutture boreliane sugli iperspazi, Tesi di Laurea, Universitá di Milano, 1993.
- Alberto Barbati, The hyperspace of an analytic metrizable space is analytic, Proceedings of the Eleventh International Conference of Topology (Trieste, 1993), 1993, pp. 15–21 (1994) (English, with English and Italian summaries). MR 1346314
- 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, Alojzy Lechicki, Sandro Levi, and Somashekhar Naimpally, Distance functionals and suprema of hyperspace topologies, Ann. Mat. Pura Appl. (4) 162 (1992), 367–381. MR 1199663, DOI 10.1007/BF01760016
- 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
- Edward G. Effros, Convergence of closed subsets in a topological space, Proc. Amer. Math. Soc. 16 (1965), 929–931. MR 181983, DOI 10.1090/S0002-9939-1965-0181983-3
- Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
- Sebastiano Francaviglia, Alojzy Lechicki, and Sandro Levi, Quasiuniformization of hyperspaces and convergence of nets of semicontinuous multifunctions, J. Math. Anal. Appl. 112 (1985), no. 2, 347–370. MR 813603, DOI 10.1016/0022-247X(85)90246-X
- 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
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2569-2574
- MSC: Primary 54B20; Secondary 54D65, 54E50
- DOI: https://doi.org/10.1090/S0002-9939-1995-1273484-5
- MathSciNet review: 1273484