| Title:
|
Compacta are maximally $G_\delta$-resolvable (English) |
| Author:
|
Juhász, István |
| Author:
|
Szentmiklóssy, Zoltán |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
259-261 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well-known that compacta (i.e. compact Hausdorff spaces) are maximally resolvable, that is every compactum $X$ contains $\Delta(X)$ many pairwise disjoint dense subsets, where $\Delta(X)$ denotes the minimum size of a non-empty open set in $X$. The aim of this note is to prove the following analogous result: Every compactum $X$ contains $\Delta_\delta(X)$ many pairwise disjoint $G_\delta$-dense subsets, where $\Delta_\delta(X)$ denotes the minimum size of a non-empty $G_\delta$ set in $X$. (English) |
| Keyword:
|
compact spaces |
| Keyword:
|
$G_\delta $-sets |
| Keyword:
|
resolvability |
| MSC:
|
03E10 |
| MSC:
|
54A25 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 06221267 |
| idMR:
|
MR3067708 |
| . |
| Date available:
|
2013-06-25T12:54:14Z |
| Last updated:
|
2015-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143274 |
| . |
| Reference:
|
[1] Čech E., Pospíšil B.: Sur les espaces compacts.Publ. Fac. Sci. Univ. Masaryk 258 (1938), 1–14. Zbl 0019.08903 |
| Reference:
|
[2] Comfort W.W., Garcia-Ferreira S.: Resolvability: A selective survey and some new results.Topology Appl. 74 (1996), 149–167. Zbl 0866.54004, MR 1425934, 10.1016/S0166-8641(96)00052-1 |
| Reference:
|
[3] El'kin A.G.: Resolvable spaces which are not maximally resolvable.Vestnik Moskov. Univ. Ser. I Mat. Meh. 24 (1969), no. 4, 66–70. Zbl 0243.54018, MR 0256331 |
| Reference:
|
[4] Juhász I.: Cardinal functions in topology – 10 years later.Mathematical Centre Tracts, 123, Mathematisch Centrum, Amsterdam, 1980. |
| Reference:
|
[5] Juhász I.: On the minimum character of points in compact spaces.in: Proc. Top. Conf. (Pécs, 1989), 365–371, Colloq. Math. Soc. János Bolyai, 55, North-Holland, Amsterdam, 1993. Zbl 0798.54005, MR 1244377 |
| Reference:
|
[6] Juhász I., Szentmiklóssy Z.: Convergent free sequences in compact spaces.Proc. Amer. Math. Soc. 116 (1992), 1153–1160. Zbl 0767.54002, MR 1137223, 10.2307/2159502 |
| . |
