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.
@article{118608,
author = {Alessandro Fedeli},
title = {On the $k$-Baire property},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {34},
year = {1993},
pages = {525-527},
zbl = {0784.54031},
mrnumber = {1243083},
language = {en},
url = {http://dml.mathdoc.fr/item/118608}
}
Fedeli, Alessandro. On the $k$-Baire property. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 525-527. http://gdmltest.u-ga.fr/item/118608/
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