Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces

R. W. Hansell; L. Oncina

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 1, page 145-155
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Hansell, R. W., and Oncina, L.. "Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces." Czechoslovak Mathematical Journal 55.1 (2005): 145-155. <http://eudml.org/doc/30933>.

@article{Hansell2005,
abstract = {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.},
author = {Hansell, R. W., Oncina, L.},
journal = {Czechoslovak Mathematical Journal},
keywords = {measurable selectors; upper semi-continuous maps; point of continuity property; measurable selectors; upper semi-continuous maps; point of continuity property},
language = {eng},
number = {1},
pages = {145-155},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces},
url = {http://eudml.org/doc/30933},
volume = {55},
year = {2005},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 145
EP - 155
AB - 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.
LA - eng
KW - measurable selectors; upper semi-continuous maps; point of continuity property; measurable selectors; upper semi-continuous maps; point of continuity property
UR - http://eudml.org/doc/30933
ER -

References

top
  1. A note on Gul’ko compact spaces, Proc. Amer. Math. Soc. 100 (1987), 371–376. (1987) Zbl0622.54020MR0884482
  2. 10.1016/0166-8641(93)90022-6, Topology Appl. 50 (1993), 217–239. (1993) Zbl0788.54036MR1227551DOI10.1016/0166-8641(93)90022-6
  3. 10.1016/0022-1236(87)90102-9, J.  Funct. Anal. 75 (1987), 382–395. (1987) Zbl0644.54014MR0916758DOI10.1016/0022-1236(87)90102-9
  4. Descriptive sets and the topology of nonseparable Banach spaces, Serdica Math.  J. 27 (2001), 1–66. (2001) Zbl0982.46012MR1828793
  5. First class functions with values in nonseparable spaces, Constantin Carathéodory: An International Tribute, Vols. I, II, World Sci. Publishing, Teaneck, 1991, pp. 461–475. (1991) Zbl0767.54010MR1130849
  6. Descriptive Topology. Recent Progress in General Topology, M.  Husec and J.  van Mill (eds.), Elsevier Science Publishers, , 1992. (1992) MR1229121
  7. First class selector for weakly upper semi-continuous multivalued maps in Banach spaces, J.  Reine Angew. Math. 361 (1985), 201–220. (1985) MR0807260
  8. 10.1006/jfan.1993.1127, J.  Funct. Anal. 117 (1993), 243–273. (1993) MR1244937DOI10.1006/jfan.1993.1127
  9. 10.1007/BF02392537, Acta. Math. 155 (1985), 41–79. (1985) MR0793237DOI10.1007/BF02392537
  10. Radon-Nikodým compact spaces and fragmentability, Mathematika 34 (1989), 258–281. (1989) MR0933504
  11. Descriptive Banach spaces and Eberlein compacta, Doctoral Thesis, Universidad de Murcia, 1999. (1999) 
  12. 10.1112/S0025579300013498, Mathematika 34 (1987), 243–257. (1987) Zbl0645.46017MR0933503DOI10.1112/S0025579300013498
  13. Baire class  1 selectors for upper-semicontinuous set-valued maps, Trans. Amer. Math. Soc. 337 (1993), 609–624. (1993) Zbl0822.54017MR1140919
  14. Pettis Integral and Measure Theory, Mem. Amer. Math. Soc. 307, Providence, 1984, pp. 224. (1984) Zbl0582.46049MR0756174

NotesEmbed ?

top

You must be logged in to post comments.