| Title:
|
Relatively compact spaces and separation properties (English) |
| Author:
|
Arhangel'skii, A. V. |
| Author:
|
Yaschenko, I. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
343-348 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the property of relative compactness of subspaces of Hausdorff spaces. Several examples of relatively compact spaces are given. We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space. (English) |
| Keyword:
|
compact space |
| Keyword:
|
separation property |
| Keyword:
|
extension |
| MSC:
|
54A25 |
| MSC:
|
54D10 |
| MSC:
|
54D15 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 0851.54024 |
| idMR:
|
MR1399005 |
| . |
| Date available:
|
2009-01-08T18:23:50Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118835 |
| . |
| Reference:
|
[AH] Arhangel'skii A.V., Hamdi M.M. Gennedi: Foundations of the theory of relative topological properties.General Topology. Spaces and mappings. MGU Moscow (1989), 3-48. |
| Reference:
|
[En] Engelking R.: General Topology.(1987), PWN Warsawa. |
| Reference:
|
[He] Herrlich H.: Ordnugsfähigkeit total-diskontinuierlicher Räume.Math. Ann. 159 (1965), 77-80. MR 0182944 |
| Reference:
|
[Jo] Jones F.B.: Hereditary separable, non-completely regular spaces.Topology Conf., Virginia Polytechnic Inst. and State U. 1973, Springer Lecture Notes in Mathematics 375 (1974), 149-152. MR 0413044 |
| Reference:
|
[PW] Porter J.R., Woods R.G.: Extensions and Absolutes of Hausdorff Spaces.Springer-Verlag (1988). Zbl 0652.54016, MR 0918341 |
| Reference:
|
[Ra] Ranchin D.B.: On compactness modulo ideal.DAN SSSR (1972), 202 761-764. MR 0296899 |
| . |
