| Title:
|
Remarks on star covering properties in pseudocompact spaces (English) |
| Author:
|
Song, Yan-Kui |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
138 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
165-169 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $P$ be a topological property. A space $X$ is said to be star $P$ if whenever $\mathcal U$ is an open cover of $X$, there exists a subspace $A\subseteq X$ with property $P$ such that $X=\mathop {\rm St}(A,\mathcal U)$, where $\mathop {\rm St}(A,\mathcal U)=\bigcup \{U\in \mathcal U\colon U\cap A\neq \emptyset \}.$ In this paper, we study the relationships of star $P$ properties for $P\in \{\textrm{Lindelöf, compact, countably compact}\}$ in pseudocompact spaces by giving some examples. (English) |
| Keyword:
|
Lindelöf |
| Keyword:
|
star Lindelöf |
| Keyword:
|
compact |
| Keyword:
|
star compact |
| Keyword:
|
countably compact |
| Keyword:
|
star countably compact space |
| MSC:
|
54A25 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 06221246 |
| idMR:
|
MR3112362 |
| DOI:
|
10.21136/MB.2013.143288 |
| . |
| Date available:
|
2013-05-27T14:24:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143288 |
| . |
| Reference:
|
[1] Alas, O. T., Junqueira, L. R., Wilson, R. G.: Countability and star covering properties.Topology Appl. 158 (2011), 620-626. Zbl 1226.54023, MR 2765618, 10.1016/j.topol.2010.12.012 |
| Reference:
|
[2] Alas, O. T., Junqueira, L. R., Mill, J. van, Tkachuk, V. V., Wilson, R. G.: On the extent of star countable spaces.Cent. Eur. J. Math. 9 (2011), 603-615. MR 2784032, 10.2478/s11533-011-0018-y |
| Reference:
|
[3] Douwen, E. K. van, Reed, G. M., Roscoe, A. W., Tree, I. J.: Star covering properties.Topology Appl. 39 (1991), 71-103. MR 1103993, 10.1016/0166-8641(91)90077-Y |
| Reference:
|
[4] Engelking, R.: General Topology.Heldermann, Berlin (1989). Zbl 0684.54001, MR 1039321 |
| Reference:
|
[5] Hiremath, G. R.: On star with Lindelöf center property.J. Indian Math. Soc., New Ser. 59 (1993), 227-242. Zbl 0887.54021, MR 1248966 |
| Reference:
|
[6] Ikenaga, S., Tani, T.: On a topological concept between countable compactness and pseudocompactness.Research Reports of Numazu Technical College 26 (1990), 139-142. |
| Reference:
|
[7] Fleischman, W. M.: A new extension of countable compactness.Fundam. Math. 67 (1970), 1-9. Zbl 0194.54601, MR 0264608, 10.4064/fm-67-1-1-9 |
| Reference:
|
[8] Matveev, M. V.: A survey on star covering properties.Topology Atlas, preprint No. 330 (1998). |
| Reference:
|
[9] Mrówka, S.: On completely regular spaces.Fundam. Math. 41 (1954), 105-106. MR 0063650, 10.4064/fm-41-1-105-106 |
| Reference:
|
[10] Song, Y.-K.: On $\Cal C$-starcompact spaces.Math. Bohem. 133 (2008), 259-266. Zbl 1199.54146, MR 2494780 |
| Reference:
|
[11] Song, Y.-K.: On $\Cal K$-starcompact spaces.Bull. Malays. Math. Sci. Soc. 30 (2007), 59-64. Zbl 1134.54314, MR 2330636 |
| Reference:
|
[12] Song, Y.-K.: On $\Cal L$-starcompact spaces.Czech. Math. J. 56 (2006), 781-788. Zbl 1164.54356, MR 2291775, 10.1007/s10587-006-0056-y |
| . |
