On a theorem of Holický and Zelený concerning Borel maps without σ -compact fibers

P. Milewski; Roman Pol

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 3, page 535-543
  • ISSN: 0011-4642

Abstract

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The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.

How to cite

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Milewski, P., and Pol, Roman. "On a theorem of Holický and Zelený concerning Borel maps without $\sigma $-compact fibers." Czechoslovak Mathematical Journal 53.3 (2003): 535-543. <http://eudml.org/doc/30797>.

@article{Milewski2003,
abstract = {The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.},
author = {Milewski, P., Pol, Roman},
journal = {Czechoslovak Mathematical Journal},
keywords = {Borel maps; $\sigma $-compact sections; set-valued maps; Borel maps; -compact sections; set-valued maps},
language = {eng},
number = {3},
pages = {535-543},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a theorem of Holický and Zelený concerning Borel maps without $\sigma $-compact fibers},
url = {http://eudml.org/doc/30797},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Milewski, P.
AU - Pol, Roman
TI - On a theorem of Holický and Zelený concerning Borel maps without $\sigma $-compact fibers
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 535
EP - 543
AB - The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.
LA - eng
KW - Borel maps; $\sigma $-compact sections; set-valued maps; Borel maps; -compact sections; set-valued maps
UR - http://eudml.org/doc/30797
ER -

References

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  5. A converse of Arsenin-Kunugui theorem on Borel sets with σ -compact sections, Fund. Math. 165 (2000), 191–202. (2000) MR1805424
  6. Classical Descriptive Set Theory, Springer-Verlag, New York, 1994. (1994) MR1321597
  7. The structure of σ -ideals of compact sets, Trans. Amer. Math. Soc. 301 (1987), 263–288. (1987) MR0879573
  8. Topology  I and II, Academic Press, Warszawa, 1966 and 1968. (1966 and 1968) MR0217751
  9. On a Hurewicz-type theorem and a selection theorem of Michael, Bull. Polish Acad. Sci. Math. 43 (1995), 273–275. (1995) MR1414783
  10. 10.1090/S0002-9939-1985-0776192-3, Proc. Amer. Math. Soc. 93 (1985), 628–632. (1985) Zbl0609.28006MR0776192DOI10.1090/S0002-9939-1985-0776192-3

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