On a selection theorem of Blum and Swaminathan

Takamitsu Yamauchi

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 4, page 681-691
  • ISSN: 0010-2628

Abstract

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Blum and Swaminathan [Pacific J. Math. 93 (1981), 251–260] introduced the notion of ℬ -fixedness for set-valued mappings, and characterized realcompactness by means of continuous selections for Tychonoff spaces of non-measurable cardinal. Using their method, we obtain another characterization of realcompactness, but without any cardinal assumption. We also characterize Dieudonné completeness and Lindelöf property in similar formulations.

How to cite

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Yamauchi, Takamitsu. "On a selection theorem of Blum and Swaminathan." Commentationes Mathematicae Universitatis Carolinae 45.4 (2004): 681-691. <http://eudml.org/doc/249370>.

@article{Yamauchi2004,
abstract = {Blum and Swaminathan [Pacific J. Math. 93 (1981), 251–260] introduced the notion of $\mathcal \{B\}$-fixedness for set-valued mappings, and characterized realcompactness by means of continuous selections for Tychonoff spaces of non-measurable cardinal. Using their method, we obtain another characterization of realcompactness, but without any cardinal assumption. We also characterize Dieudonné completeness and Lindelöf property in similar formulations.},
author = {Yamauchi, Takamitsu},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {set-valued mapping; selection; realcompact; Dieudonné complete; Lindelöf; $\mathcal \{B\}$-fixed; local intersection property; open lower sections; realcompact space; Dieudonné complete space; Lindelöf space; continuous selection; lower semicontinuous set-valued mapping},
language = {eng},
number = {4},
pages = {681-691},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a selection theorem of Blum and Swaminathan},
url = {http://eudml.org/doc/249370},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Yamauchi, Takamitsu
TI - On a selection theorem of Blum and Swaminathan
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 4
SP - 681
EP - 691
AB - Blum and Swaminathan [Pacific J. Math. 93 (1981), 251–260] introduced the notion of $\mathcal {B}$-fixedness for set-valued mappings, and characterized realcompactness by means of continuous selections for Tychonoff spaces of non-measurable cardinal. Using their method, we obtain another characterization of realcompactness, but without any cardinal assumption. We also characterize Dieudonné completeness and Lindelöf property in similar formulations.
LA - eng
KW - set-valued mapping; selection; realcompact; Dieudonné complete; Lindelöf; $\mathcal {B}$-fixed; local intersection property; open lower sections; realcompact space; Dieudonné complete space; Lindelöf space; continuous selection; lower semicontinuous set-valued mapping
UR - http://eudml.org/doc/249370
ER -

References

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  2. Blum I., Swaminathan S., Continuous selections and realcompactness, Pacific J. Math. 93 (1981), 251-260. (1981) Zbl0457.54012MR0623561
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  8. Nedev S., Selection and factorization theorems for set-valued mappings, Serdica 6 (1980), 291-317. (1980) Zbl0492.54006MR0644284
  9. Repovš D., Semenov P.V., Continuous selections of multivalued mappings, Kluwer Acad. Publ., Dordrecht, 1998. MR1659914
  10. Tamano H., On compactifications, J. Math. Kyoto Univ. 1 (1962), 162-193. (1962) Zbl0106.15601MR0142096
  11. Wiscamb M.R., The discrete countable chain condition, Proc. Amer. Math. Soc. 23 (1969), 608-612. (1969) Zbl0184.26304MR0248744
  12. Wu X., Shen S., A further generalization of Yannelis-Prabhakar's continuous selection theorem and its applications, J. Math. Anal. Appl. 197 (1996), 61-74. (1996) Zbl0852.54019MR1371276
  13. Yannelis N.C., Prabhakar N.D., Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econom. 12 (1983), 233-245. (1983) Zbl0536.90019MR0743037

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