| Title:
|
Minimal $KC$-spaces are countably compact (English) |
| Author:
|
Vidalis, T. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
543-547 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we show that a minimal space in which compact subsets are closed is countably compact. This answers a question posed in [1]. (English) |
| Keyword:
|
$K$C-space |
| Keyword:
|
weaker topology |
| MSC:
|
54A10 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 1097.54027 |
| idMR:
|
MR2103148 |
| . |
| Date available:
|
2009-05-05T16:47:18Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119481 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/133424 |
| . |
| Reference:
|
[1] Alas O.T., Wilson R.G.: Spaces in which compact subsets are closed and the lattice of $T_1$-topologies on a set.Comment. Math. Univ. Carolinae 43.4 (2002), 641-652. Zbl 1090.54015, MR 2045786 |
| Reference:
|
[2] Fleissner W.G.: A $T_B$-space which is not Katětov $T_B$.Rocky Mountain J. Math. 10 (1980), 661-663. Zbl 0448.54021, MR 0590229 |
| Reference:
|
[3] Hewitt E.: A problem of set theoretic topology.Duke Math. J. 10 (1943), 309-333. Zbl 0060.39407, MR 0008692 |
| Reference:
|
[4] Larson R.: Complementary topological properties.Notices AMS 20 (1973), 176. |
| Reference:
|
[5] Ramanathan A.: Minimal bicompact spaces.J. Indian Math. Soc. 19 (1948), 40-46. Zbl 0041.51502, MR 0028010 |
| Reference:
|
[6] Smythe N., Wilkins C.A.: Minimal Hausdorff and maximal compact spaces.J. Austral. Math. Soc. 3 (1963), 167-177. Zbl 0163.17201, MR 0154254 |
| Reference:
|
[7] Tong H.: Minimal bicompact spaces.Bull. Amer. Math. Soc. 54 (1948), 478-479. |
| . |
