| Title:
|
Short proofs of two theorems in topology (English) |
| Author:
|
Ismail, M. |
| Author:
|
Szymański, A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
539-541 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A $T_1$ weakly $\delta \theta $-refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential. (English) |
| Keyword:
|
countably compact |
| Keyword:
|
initially $\kappa $-compact |
| Keyword:
|
weakly $\delta \theta $-refinable |
| Keyword:
|
$\kappa $-refinable |
| Keyword:
|
sequential |
| MSC:
|
54D20 |
| MSC:
|
54D30 |
| MSC:
|
54D55 |
| idZBL:
|
Zbl 0780.54023 |
| idMR:
|
MR1243085 |
| . |
| Date available:
|
2009-01-08T18:05:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118610 |
| . |
| Reference:
|
[A] Arhangel'skiĭ A.V.: The star method, new classes of spaces and countable compactness.Soviet Math. Dokl. 21 (1980), 550-554. MR 0569369 |
| Reference:
|
[B] Burke D.K.: Covering properties.Handbook of Set Theoretic Topology, North Holland, 1984, pp. 347-422. Zbl 0569.54022, MR 0776628 |
| Reference:
|
[O] Ostaszewski A.J.: Compact $\sigma $-metric Hausdorff spaces are sequential.Proc. Amer. Math. Soc. 68 (1978), 339-343. Zbl 0392.54014, MR 0467677 |
| Reference:
|
[S] Stephenson R.M., Jr.: Initially $\kappa $-compact and related spaces.Handbook of Set Theoretic Topology, North Holland (1984), pp. 603-632. Zbl 0588.54025, MR 0776632 |
| Reference:
|
[WW] Wicke H.H., Worrell J.M., Jr.: Point countability and compactness.Proc. Amer. Math. Soc. 55 (1976), 427-431. Zbl 0323.54013, MR 0400166 |
| . |
