On Baireness of the Wijsman Hyperspace
Zsilinszky, László
Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 1071-1079 / Harvested from Biblioteca Digitale Italiana di Matematica

Baireness of the Wijsman hyperspace topology is characterized for a me- trizable base space with a countable-in-itself p-base; further a separable 1st category metric space is constructed with a Baire Wijsman hyperspace.

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.

Publié le : 2007-10-01
@article{BUMI_2007_8_10B_3_1071_0,
     author = {L\'aszl\'o Zsilinszky},
     title = {On Baireness of the Wijsman Hyperspace},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {1071-1079},
     zbl = {1181.54019},
     mrnumber = {2507914},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_1071_0}
}
Zsilinszky, László. On Baireness of the Wijsman Hyperspace. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 1071-1079. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_1071_0/

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

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

[3] Beer, G., Topologies on Closed and Closed Convex Sets, Kluwer, Dordrecht, 1993. | MR 1269778 | Zbl 0792.54008

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

[5] Beer, G. - Lechicki, A. - Levi, S. - Naimpally, S., Distance Functionals and Suprema of Hyperspace Topologies, Annali Mat. Pura Appl., 162 (1992), 367-381. | MR 1199663 | Zbl 0774.54004

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

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

[8] Costantini, C. - Levi, S. - Pelant, J., Infima of hyperspace topologies, Mathematika, 42 (1995), 67-86. | MR 1346673 | Zbl 0822.54004

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

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

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

[12] Haworth, R. C. - Mccoy, R. A., Baire spaces, Dissertationes Math., 141 (1977), 1- 77. | MR 431104

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

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

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

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

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

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

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

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

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