| Title:
|
Two improvements on Tkačenko's addition theorem (English) |
| Author:
|
Gerlits, J. |
| Author:
|
Juhász, I. |
| Author:
|
Szentmiklóssy, Z. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
705-710 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that (A) if a countably compact space is the union of countably many $D$ subspaces then it is compact; (B) if a compact $T_2$ space is the union of fewer than $N(\Bbb R)$ = $\operatorname{cov} (\Cal M)$ left-separated subspaces then it is scattered. Both (A) and (B) improve results of Tkačenko from 1979; (A) also answers a question that was raised by Arhangel'ski\v{i} and improves a result of Gruenhage. (English) |
| Keyword:
|
$D$-space |
| Keyword:
|
left separated |
| Keyword:
|
compact |
| Keyword:
|
countably compact |
| Keyword:
|
scattered space |
| Keyword:
|
Novák number |
| MSC:
|
54A25 |
| MSC:
|
54D55 |
| MSC:
|
54G12 |
| idZBL:
|
Zbl 1121.54041 |
| idMR:
|
MR2259500 |
| . |
| Date available:
|
2009-05-05T16:54:26Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119560 |
| . |
| Reference:
|
[1] Arhangel'skii A.V.: $D$-spaces and covering properties.Topology Appl. 146-147 (2005), 437-449. Zbl 1063.54013, MR 2107163 |
| Reference:
|
[2] Gerlits J., Juhász I.: On left-separated compact spaces.Comment. Math. Univ. Carolinae 19 (1978), 53-62. MR 0487982 |
| Reference:
|
[3] Gruenhage G.: A note on $D$-spaces.preprint. Zbl 1101.54029, MR 2238727 |
| Reference:
|
[4] Juhász I., Shelah S.: $\pi (X) = \delta (X)$ for compact $X$.Topology Appl. 32 (1989), 289-294. Zbl 0688.54002, MR 1007107 |
| Reference:
|
[5] Simon P.: Left-separated spaces: a comment to a paper of M.G. Tkačenko.Comment. Math. Univ. Carolinae 20 (1979), 597-603. MR 0550459 |
| Reference:
|
[6] Tkačenko M.G.: O bikompaktah predstavimyh v vide obedidenia schetnogo chisla levych podprostranstv I, II.Comment. Math. Univ. Carolinae 20 (1979), 361-379 and 381-395. MR 0539565 |
| Reference:
|
[7] van Douwen E., Pfeffer W.F.: Some properties of the Sorgenfrey-line and related spaces.Pacific J. Math. 81 (1979), 371-377. Zbl 0409.54011, MR 0547605 |
| Reference:
|
[8] Weston J.H., Shilleto J.: Cardinalities of dense sets.Gen. Topology Appl. 6 (1976), 227-240. Zbl 0321.54003, MR 0442875 |
| . |
