| Title:
|
On $\scr L$-starcompact spaces (English) |
| Author:
|
Song, Yan-Kui |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
781-788 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A space $X$ is $\mathcal L$-starcompact if for every open cover $\mathcal U$ of $X,$ there exists a Lindelöf subset $L$ of $X$ such that $\mathop {\mathrm St}(L,{\mathcal U})=X.$ We clarify the relations between ${\mathcal L}$-starcompact spaces and other related spaces and investigate topological properties of ${\mathcal L}$-starcompact spaces. A question of Hiremath is answered. (English) |
| Keyword:
|
Lindelöf |
| Keyword:
|
star-Lindelöf and ${\mathcal L}$-starcompact |
| MSC:
|
54B10 |
| MSC:
|
54D20 |
| MSC:
|
54D55 |
| idZBL:
|
Zbl 1164.54356 |
| idMR:
|
MR2291775 |
| . |
| Date available:
|
2009-09-24T11:38:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128105 |
| . |
| Reference:
|
[1] E. K. van Douwen, G. M. Reed, A. W. Roscoe and I. J. Tree: Star covering properties.Topology Appl. 39 (1991), 71–103. MR 1103993, 10.1016/0166-8641(91)90077-Y |
| Reference:
|
[2] R. Engelking: General Topology, Revised and completed edition.Heldermann Verlag, Berlin, 1989. MR 1039321 |
| Reference:
|
[3] G. R. Hiremath: On star with Lindelöf center property.J. Indian Math. Soc. 59 (1993), 227–242. Zbl 0887.54021, MR 1248966 |
| Reference:
|
[4] S. Ikenaga: A class which contains Lindelöf spaces, separable spaces and countably compact spaces.Memories of Numazu College of Technology 18 (1983), 105–108. |
| Reference:
|
[5] R. C. Walker: The Stone-Čech compactification.Berlin, 1974. Zbl 0292.54001, MR 0380698 |
| Reference:
|
[6] M. V. Matveev: A survey on star-covering properties.Topological Atlas, preprint No. 330, 1998. |
| Reference:
|
[7] S. Mrówka: On complete regular spaces.Fund. Math. 41 (1954), 105–106. |
| Reference:
|
[8] Y. Yasui and Z. Gao: Space in countable web.Houston J. Math. 25 (1999), 327–325. MR 1697629 |
| . |
