Geodesic
Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 145-155
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 46B22, 46B99, 47H04
Keywords: measurable selectors; upper semi-continuous maps; point of continuity property 
@article{CMJ_2005_55_1_a9,
     author = {Hansell, R. W. and Oncina, L.},
     title = {Generalized first class selectors for upper semi-continuous set-valued maps in {Banach} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {145--155},
     year = {2005},
     volume = {55},
     number = {1},
     mrnumber = {2121662},
     zbl = {1081.46016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a9/}
}
TY  - JOUR
AU  - Hansell, R. W.
AU  - Oncina, L.
TI  - Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2005
SP  - 145
EP  - 155
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a9/
LA  - en
ID  - CMJ_2005_55_1_a9
ER  - 
%0 Journal Article
%A Hansell, R. W.
%A Oncina, L.
%T Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces
%J Czechoslovak Mathematical Journal
%D 2005
%P 145-155
%V 55
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a9/
%G en
%F CMJ_2005_55_1_a9
Hansell, R. W.; Oncina, L. Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 145-155. http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a9/

[1] G. Gruenhage: A note on Gul’ko compact spaces. Proc. Amer. Math. Soc. 100 (1987), 371–376. | MR | Zbl

[2] G. Koumoullis: A generalization of functions of the first class. Topology Appl. 50 (1993), 217–239. | DOI | MR | Zbl

[3] W. R. Hansell: First class selectors for upper semi-continuous multifunctions. J.  Funct. Anal. 75 (1987), 382–395. | DOI | MR | Zbl

[4] R. W. Hansell: Descriptive sets and the topology of nonseparable Banach spaces. Serdica Math.  J. 27 (2001), 1–66. | MR | Zbl

[5] R. W. Hansell: First class functions with values in nonseparable spaces. Constantin Carathéodory: An International Tribute, Vols. I, II, World Sci. Publishing, Teaneck, 1991, pp. 461–475. | MR | Zbl

[6] R. W. Hansell: Descriptive Topology. Recent Progress in General Topology. M.  Husec and J.  van Mill (eds.), Elsevier Science Publishers, , 1992. | MR

[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. | MR

[8] J. E. Jayne, J. Orihuela, A. J. Pallarés, and G. Vera: $\sigma $-fragmentability of multivalued maps and selection theorems. J.  Funct. Anal. 117 (1993), 243–273. | DOI | MR

[9] J. E. Jayne, C. A. Rogers: Borel selectors for upper semi-continuous set-valued maps. Acta. Math. 155 (1985), 41–79. | DOI | MR

[10] I. Namioka: Radon-Nikodým compact spaces and fragmentability. Mathematika 34 (1989), 258–281. | MR

[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. | DOI | MR | Zbl

[13] V. V. Srivatsa: Baire class  1 selectors for upper-semicontinuous set-valued maps. Trans. Amer. Math. Soc. 337 (1993), 609–624. | MR | Zbl

[14] M. Talagrand: Pettis Integral and Measure Theory. Mem. Amer. Math. Soc. 307, Providence, 1984, pp. 224. | MR | Zbl