| Title:
|
On the $k$-Baire property (English) |
| Author:
|
Fedeli, Alessandro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
525-527 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$k$-Baire |
| Keyword:
|
almost $k$-discrete |
| Keyword:
|
point-$k$ |
| Keyword:
|
locally-$k$ |
| MSC:
|
54D20 |
| MSC:
|
54E52 |
| MSC:
|
54E65 |
| MSC:
|
54G10 |
| MSC:
|
54G99 |
| idZBL:
|
Zbl 0784.54031 |
| idMR:
|
MR1243083 |
| . |
| Date available:
|
2009-01-08T18:05:48Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118608 |
| . |
| Reference:
|
[1] Fletcher P., Lindgren W.F.: A note on spaces of second category.Arch. der Math. 24 (1973), 186-187. Zbl 0259.54019, MR 0315663 |
| Reference:
|
[2] Fogelgren J.R., McCoy R.A.: Some topological properties defined by homeomorphism groups.Arch. der Math. 22 (1971), 528-533. Zbl 0245.54018, MR 0300259 |
| Reference:
|
[3] Haworth R.C., McCoy R.A.: Baire spaces.Dissertationes Math. 141 (1977), 1-73. Zbl 0344.54001, MR 0431104 |
| Reference:
|
[4] Levy R.: Almost $P$-spaces.Can. J. Math. 29 (1977), 284-288. Zbl 0342.54032, MR 0464203 |
| Reference:
|
[5] Tall F.D.: The countable chain condition versus separability - applications of Martin's axiom.Gen. Top. and Appl. 4 (1974), 315-339. Zbl 0293.54003, MR 0423284 |
| Reference:
|
[6] Walker R.C.: The Stone-Čech compactification.Springer-Verlag, 1974. Zbl 0292.54001, MR 0380698 |
| Reference:
|
[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. Zbl 0571.54005, MR 0776638 |
| . |
