Geodesic
On the $k$-Baire property
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 525-527

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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 $\Cal U$ of $X$ such that $\operatorname{card}\, (\Cal U)\leq k$ 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.
Classification : 54D20, 54E52, 54E65, 54G10, 54G99
Keywords: $k$-Baire; almost $k$-discrete; point-$k$; locally-$k$ 
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Fedeli, Alessandro. On the $k$-Baire property. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 525-527. http://geodesic.mathdoc.fr/item/CMUC_1993__34_3_a13/