Consonance and Cantor set-selectors

• Autorzy: Valentin Gutev
• Języki publikacji: EN

Abstrakty

EN

It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.

Słowa kluczowe

EN

Set-valued mapping; Lower (upper) semi-continuous; Selection; Section; Consonant space

Kategorie tematyczne

• 54C60: Set-valued maps
• 54B20: Hyperspaces
• 54C65: Selections

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 2
• Strony: 341-348

Daty

wydano

2013-02-01

online

2012-11-21

Twórcy

autor

Valentin Gutev

• University of Malta

Bibliografia

• [1] Alleche B., Calbrix J., On the coincidence of the upper Kuratowski topology with the cocompact topology, Topology Appl., 1999, 93(3), 207–218 http://dx.doi.org/10.1016/S0166-8641(97)00269-1
• [2] Banakh T.O., Topology of spaces of probability measures. I. The functors P τ and P̃, Mat. Stud., 1995, 5, 65–87 (in Russian)
• [3] Borges C.J.R., A study of multivalued functions, Pacific J. Math., 1967, 23, 451–461
• [4] Bouziad A., Borel measures in consonant spaces, Topology Appl., 1996, 70(2–3), 125–132 http://dx.doi.org/10.1016/0166-8641(95)00089-5
• [5] Bouziad A., A note on consonance of P δ subsets, Topology Appl., 1998, 87(1), 53–61 http://dx.doi.org/10.1016/S0166-8641(97)00131-4
• [6] Bouziad A., Consonance and topological completeness in analytic spaces, Proc. Amer. Math. Soc., 1999, 127(12), 3733–3737 http://dx.doi.org/10.1090/S0002-9939-99-04902-3
• [7] Bouziad A., Filters, consonance and hereditary Baireness, Topology Appl., 2000, 104(1–3), 27–38 http://dx.doi.org/10.1016/S0166-8641(99)00014-0
• [8] Choban M.M., Many-valued mappings and Borel sets. I, Trans. Moscow Math. Soc., 1970, 22, 258–280
• [9] Costantini C., Watson S., On the dissonance of some metrizable spaces, Topology Appl., 1998, 84(1–3), 259–268 http://dx.doi.org/10.1016/S0166-8641(97)00096-5
• [10] Debs G., Espaces héréditairement de Baire, Fund. Math., 1988, 129(3), 199–206
• [11] Dolecki S., Greco G.H., Lechicki A., Sur la topologie de la convergence supérieure de Kuratowski, C. R. Acad. Sci. Paris, 1991, 312(12), 923–926
• [12] Dolecki S., Greco G.H., Lechicki A., When do the upper Kuratowski topology (homeomorphically, Scott topology) and the co-compact topology coincide?, Trans. Amer. Math. Soc., 1995, 347(8), 2869–2884 http://dx.doi.org/10.1090/S0002-9947-1995-1303118-7
• [13] El’kin A.G., A-sets in complete metric spaces, Dokl. Akad. Nauk SSSR, 1967, 175, 517–520
• [14] Gutev V., Selections and approximations in finite-dimensional spaces, Topology Appl., 2005, 146–147, 353–383 http://dx.doi.org/10.1016/j.topol.2003.06.002
• [15] Gutev V., Completeness, sections and selections, Set-Valued Anal., 2007, 15(3), 275–295 http://dx.doi.org/10.1007/s11228-007-0041-0
• [16] Gutev V., Nedev S., Pelant J., Valov V., Cantor set selectors, Topology Appl., 1992, 44(1–3), 163–166 http://dx.doi.org/10.1016/0166-8641(92)90089-I
• [17] Gutev V., Valov V., Sections, selections and Prohorov’s theorem, J. Math. Anal. Appl., 2009, 360(2), 377–379 http://dx.doi.org/10.1016/j.jmaa.2009.06.063
• [18] Koumoullis G., Cantor sets in Prohorov spaces, Fund. Math., 1984, 124(2), 155–161
• [19] Kuratowski K., Topology. I, Academic Press, New York-London; PWN, Warsaw, 1966
• [20] Michael E., Continuous selections. I, Ann. of Math., 1956, 63, 361–382 http://dx.doi.org/10.2307/1969615
• [21] Michael E., Continuous selections. II, Ann. of Math., 1956, 64, 562–580 http://dx.doi.org/10.2307/1969603
• [22] Michael E., A theorem on semi-continuous set-valued functions, Duke Math. J., 1959, 26, 647–651 http://dx.doi.org/10.1215/S0012-7094-59-02662-6
• [23] van Mill J., Pelant J., Pol R., Selections that characterize topological completeness, Fund. Math., 1996, 149(2), 127–141
• [24] Nedev S.J., Valov V.M., On metrizability of selectors, C. R. Acad. Bulgare Sci., 1983, 36(11), 1363–1366
• [25] Nogura T., Shakhmatov D., When does the Fell topology on a hyperspace of closed sets coincide with the meet of the upper Kuratowski and the lower Vietoris topologies?, Topology Appl., 1996, 70(2–3), 213–243 http://dx.doi.org/10.1016/0166-8641(95)00098-4
• [26] Preiss D., Metric spaces in which Prohorov’s theorem is not valid, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 1973, 27, 109–116 http://dx.doi.org/10.1007/BF00536621
• [27] Prokhorov Yu.V., Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl., 1956, 1(2), 157–214 http://dx.doi.org/10.1137/1101016
• [28] Przymusinski T., Collectionwise normality and absolute retracts, Fund. Math., 1978, 98(1), 61–73
• [29] Scott D., Continuous lattices, In: Toposes, Algebraic Geometry and Logic, Halifax, January 16–19, 1971, Lecture Notes in Math., 274, Springer, Berlin, 1972, 97–136 http://dx.doi.org/10.1007/BFb0073967
• [30] Stone A.H., On σ-discreteness and Borel isomorphism, Amer. J. Math., 1963, 85, 655–666 http://dx.doi.org/10.2307/2373113

Identyfikatory

DOI

10.2478/s11533-012-0137-0