| Title:
|
On relatively almost countably compact subsets (English) |
| Author:
|
Song, Yan-Kui |
| Author:
|
Zheng, Shu-Nian |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
135 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
291-297 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subset $Y$ of a space $X$ is almost countably compact in $X$ if for every countable cover $\Cal U$ of $Y$ by open subsets of $X$, there exists a finite subfamily $\Cal V$ of $\Cal U$ such that $Y\subseteq \overline {\bigcup \Cal V}$. In this paper we investigate the relationship between almost countably compact spaces and relatively almost countably compact subsets, and also study various properties of relatively almost countably compact subsets. (English) |
| Keyword:
|
countably compact space |
| Keyword:
|
almost countably compact space |
| Keyword:
|
relatively almost countably compact subset |
| MSC:
|
54D15 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 1224.54054 |
| idMR:
|
MR2683640 |
| DOI:
|
10.21136/MB.2010.140705 |
| . |
| Date available:
|
2010-07-20T18:45:29Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140705 |
| . |
| Reference:
|
[1] Bonanzinga, M., Matveev, M. V., Pareek, C. M.: Some remarks on generalizations of countably compact spaces and Lindelöf spaces.Rend. Circ. Mat. Palermo (2) 51 (2002), 163-174. Zbl 1194.54008, MR 1905715, 10.1007/BF02871459 |
| Reference:
|
[2] Engelking, R.: General Topology.Heldermann Berlin (1989). Zbl 0684.54001, MR 1039321 |
| Reference:
|
[3] Mashhour, A. S., El-Monsef, M. E. Abd, El-Deeb, S. N.: On precontinuous and weak precontinuous mappings.Proc. Math. Phys. Soc. Egypt 53 (1983), 47-53. MR 0830896 |
| Reference:
|
[4] Sarsak, M. S.: On relatively almost Lindelöf subsets.Acta Math. Hungar 97 (2002), 109-114. Zbl 1006.54030, MR 1932797, 10.1023/A:1020811012865 |
| Reference:
|
[5] Song, Y.-K.: On almost countably compact spaces.Preprint. |
| Reference:
|
[6] Wilansky, A.: Topics in Functional Analysis.Springer Berlin (1967). Zbl 0156.36103, MR 0223854 |
| . |
