On the k -Baire property

Alessandro Fedeli

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 3, page 525-527
  • ISSN: 0010-2628

Abstract

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In this note we show the following theorem: “Let X be an almost k -discrete space, where k is a regular cardinal. Then X is k + -Baire iff it is a k -Baire space and every point- k open cover 𝒰 of X such that card ( 𝒰 ) ≤ k is locally- k at a dense set of points.” For k = ℵ 0 we obtain a well-known characterization of Baire spaces. The case k = ℵ 1 is also discussed.

How to cite

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Fedeli, Alessandro. "On the $k$-Baire property." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 525-527. <http://eudml.org/doc/247462>.

@article{Fedeli1993,
abstract = {In this note we show the following theorem: “Let $X$ be an almost $k$-discrete space, where $k$ is a regular cardinal. Then $X$ is $k^+$-Baire iff it is a $k$-Baire space and every point-$k$ open cover $\mathcal \{U\}$ of $X$ such that $\operatorname\{card\}\, (\mathcal \{U\})\le k$ is locally-$k$ at a dense set of points.” For $k=\aleph _0$ we obtain a well-known characterization of Baire spaces. The case $k=\aleph _1$ is also discussed.},
author = {Fedeli, Alessandro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$k$-Baire; almost $k$-discrete; point-$k$; locally-$k$; -Baire space; point- open cover},
language = {eng},
number = {3},
pages = {525-527},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the $k$-Baire property},
url = {http://eudml.org/doc/247462},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Fedeli, Alessandro
TI - On the $k$-Baire property
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 3
SP - 525
EP - 527
AB - In this note we show the following theorem: “Let $X$ be an almost $k$-discrete space, where $k$ is a regular cardinal. Then $X$ is $k^+$-Baire iff it is a $k$-Baire space and every point-$k$ open cover $\mathcal {U}$ of $X$ such that $\operatorname{card}\, (\mathcal {U})\le k$ is locally-$k$ at a dense set of points.” For $k=\aleph _0$ we obtain a well-known characterization of Baire spaces. The case $k=\aleph _1$ is also discussed.
LA - eng
KW - $k$-Baire; almost $k$-discrete; point-$k$; locally-$k$; -Baire space; point- open cover
UR - http://eudml.org/doc/247462
ER -

References

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  2. Fogelgren J.R., McCoy R.A., Some topological properties defined by homeomorphism groups, Arch. der Math. 22 (1971), 528-533. (1971) Zbl0245.54018MR0300259
  3. Haworth R.C., McCoy R.A., Baire spaces, Dissertationes Math. 141 (1977), 1-73. (1977) Zbl0344.54001MR0431104
  4. Levy R., Almost P -spaces, Can. J. Math. 29 (1977), 284-288. (1977) Zbl0342.54032MR0464203
  5. Tall F.D., The countable chain condition versus separability - applications of Martin's axiom, Gen. Top. and Appl. 4 (1974), 315-339. (1974) Zbl0293.54003MR0423284
  6. Walker R.C., The Stone-Čech compactification, Springer-Verlag, 1974. Zbl0292.54001MR0380698
  7. Weiss W., Versions of Martin's axiom, in ``Handbook of Set-Theoretic Topology'', (K. Kunen and J.E. Vaughan, eds.), Elsevier Science Publishers, B.V., North Holland, 1984, pp. 827-886. Zbl0571.54005MR0776638

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