×

zbMATH — the first resource for mathematics

Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces. (English) Zbl 1081.46016
Summary: In this paper, we deal with weakly upper semi-continuous set-valued maps, taking arbitrary non-empty values, from a non-metric domain to a Banach space. We obtain selectors having the point of continuity property relative to the norm topology for a large class of compact spaces as a domain. Exact conditions under which the selector is of the first Borel class are also investigated.
MSC:
46B22 Radon-Nikodým, Kreĭn-Milman and related properties
PDF BibTeX XML Cite
Full Text: DOI EuDML Link
References:
[1] G. Gruenhage: A note on Gul?ko compact spaces. Proc. Amer. Math. Soc. 100 (1987), 371-376. · Zbl 0622.54020
[2] G. Koumoullis: A generalization of functions of the first class. Topology Appl. 50 (1993), 217-239. · Zbl 0788.54036
[3] W. R. Hansell: First class selectors for upper semi-continuous multifunctions. J. Funct. Anal. 75 (1987), 382-395. · Zbl 0644.54014
[4] R. W. Hansell: Descriptive sets and the topology of nonseparable Banach spaces. Serdica Math. J. 27 (2001), 1-66. · Zbl 0982.46012
[5] R. W. Hansell: First class functions with values in nonseparable spaces. Constantin Carath?odory: An International Tribute, Vols. I, II. World Sci. Publishing, Teaneck, 1991, pp. 461-475.
[6] R. W. Hansell: Descriptive Topology. Recent Progress in General Topology (M. Husec and J. van Mill, eds.). Elsevier Science Publishers, 1992.
[7] R. W. Hansell, J. E. Jayne, and M. Talagrand: First class selector for weakly upper semi-continuous multivalued maps in Banach spaces. J. Reine Angew. Math. 361 (1985), 201-220; 362 (1986), 219-220. · Zbl 0573.54012
[8] J. E. Jayne, J. Orihuela, A. J. Pallar?s, and G. Vera: ?-fragmentability of multivalued maps and selection theorems. J. Funct. Anal. 117 (1993), 243-273. · Zbl 0822.54018
[9] J. E. Jayne, C. A. Rogers: Borel selectors for upper semi-continuous set-valued maps. Acta. Math. 155 (1985), 41-79. · Zbl 0588.54020
[10] I. Namioka: Radon-Nikod?m compact spaces and fragmentability. Mathematika 34 (1989), 258-281. · Zbl 0654.46017
[11] L. Oncina: Descriptive Banach spaces and Eberlein compacta. Doctoral Thesis. Universidad de Murcia, 1999.
[12] N. K. Ribarska: Internal characterization of fragmentable spaces. Mathematika 34 (1987), 243-257. · Zbl 0645.46017
[13] V.V. Srivatsa: Baire class 1 selectors for upper-semicontinuous set-valued maps. Trans. Amer. Math. Soc. 337 (1993), 609-624. · Zbl 0822.54017
[14] M. Talagrand: Pettis Integral and Measure Theory. Mem. Amer. Math. Soc. 307, Providence, 1984, pp. 224. · Zbl 0582.46049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.