Zsilinszky: On Baireness of the Wijsman Hyperspace

Zsilinszky, László:
On Baireness of the Wijsman Hyperspace
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.3, p. 1071-1079, Unione Matematica Italiana (English)
È corretto da BUMI_2009_9_2_3_575_0 | pdf (384 Kb), djvu (95 Kb). | MR 2507914 | Zbl 1181.54019

Sunto

Si fornisce una caratterizzazione della proprietà di essere di Baire per la topologia di Wijsman nell'ipotesi in cui lo spazio di base sia quasi localmente separabile e metrizzabile. Si esibisce inoltre un esempio di spazio metrico di prima categoria la cui topologia di Wijsman risulta essere di Baire.

Referenze Bibliografiche

[1] A. BARBATI, The hyperspace of an analytic metrizable space is analytic, Rend. Ist. Mat. Univ. Trieste, 25 (1993), 15-21. | MR 1346314 | Zbl 0849.54030

[2] G. BEER, A Polish topology for the closed subsets of a Polish space, Proc. Amer. Math. Soc., 113 (1991), 1123-1133. | fulltext (doi) | MR 1065940 | Zbl 0776.54011

[3] G. BEER, Topologies on Closed and Closed Convex Sets, Kluwer, Dordrecht, 1993. | fulltext (doi) | MR 1269778 | Zbl 0792.54008

[4] R. H. BING, Extending a metric, Duke Math. J., 14 (1947), 511-519. | MR 24609 | Zbl 0030.08003

[5] G. BEER - A. LECHICKI - S. LEVI - S. NAIMPALLY, Distance Functionals and Suprema of Hyperspace Topologies, Annali Mat. Pura Appl., 162 (1992), 367-381. | fulltext (doi) | MR 1199663 | Zbl 0774.54004

[6] C. COSTANTINI, Every Wijsman topology relative to a Polish space is Polish, Proc. Amer. Math. Soc., 123 (1995), 2569-2574. | fulltext (doi) | MR 1273484 | Zbl 0831.54014

[7] C. COSTANTINI, On the hyperspace of a non-separable metric space, Proc. Amer. Math. Soc., 126 (1998), 3393-3396. | fulltext (doi) | MR 1618729 | Zbl 0898.54012

[8] C. COSTANTINI - S. LEVI - J. PELANT, Infima of hyperspace topologies, Mathematika, 42 (1995), 67-86. | fulltext (doi) | MR 1346673 | Zbl 0822.54004

[9] J. CHABER - R. POL, Note on the Wijsman hyperspaces of completely metrizable spaces, Bollettino U.M.I., 85-B (2002), 827-832. | fulltext bdim | fulltext EuDML | MR 1934383 | Zbl 1098.54006

[10] E. G. EFFROS, Convergence of closed subsets in a topological space, Proc. Amer. Math. Soc., 16 (1965), 929-931. | fulltext (doi) | MR 181983 | Zbl 0139.40403

[11] L'. HOLÁ - R. LUCCHETTI, Equivalence among hypertopologies, Set-Valued Anal., 3 (1995), 339-350. | fulltext (doi) | MR 1372872

[12] R. C. HAWORTH - R. A. MCCOY, Baire spaces, Dissertationes Math., 141 (1977), 1- 77. | fulltext EuDML | MR 431104

[13] T. NEUBRUNN, A note on mappings of Baire spaces, Math. Slovaca, 27 (1977), 173-176. | fulltext EuDML | MR 454910 | Zbl 0371.54023

[14] J. C. OXTOBY, Cartesian products of Baire spaces, Fundam. Math., 49 (1961), 157-166. | fulltext EuDML | fulltext (doi) | MR 140638 | Zbl 0113.16402

[15] Z. PIOTROWSKI - A. ROSANOWSKI - B. M. SCOTT, The pinched-cube topology, Pacific J. Math., 105 (1983), 399-413. | MR 691611 | Zbl 0516.54006

[16] A. TODD, Quasiregular, pseudocomplete, and Baire spaces, Pacific J. Math., 95 (1981), 233-250. | MR 631673

[17] R. WIJSMAN, Convergence of sequences of convex sets, cones and functions II, Trans. Amer. Math. Soc., 123 (1966), 32-45. | fulltext (doi) | MR 196599 | Zbl 0146.18204

[18] L. ZSILINSZKY, Baire spaces and hyperspace topologies, Proc. Amer. Math. Soc., 124 (1996), 2575-2584. | fulltext (doi) | MR 1343733 | Zbl 0855.54011

[19] L. ZSILINSZKY, Polishness of the Wijsman topology revisited, Proc. Amer. Math. Soc., 126 (1998), 3763-3765. | fulltext (doi) | MR 1458275 | Zbl 0899.54009

[20] L. ZSILINSZKY, Topological Games and Hyperspace Topologies, Set-Valued Anal., 6 (1998), 187-207. | fulltext (doi) | MR 1646498 | Zbl 0910.54011

[21] L. ZSILINSZKY, Products of Baire spaces revisited, Fundam. Math., 183 (2004), 115-121. | fulltext EuDML | fulltext (doi) | MR 2127961 | Zbl 1076.54024

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche