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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