| Title:
|
Which topological spaces have a weak reflection in compact spaces? (English) |
| Author:
|
Kovár, Martin Maria |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
529-536 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The problem, whether every topological space has a weak compact reflection, was answered by M. Hu\v sek in the negative. Assuming normality, M. Hu\v sek fully characterized the spaces having a weak reflection in compact spaces as the spaces with the finite Wallman remainder. In this paper we prove that the assumption of normality may be omitted. On the other hand, we show that some covering properties kill the weak reflectivity of a noncompact topological space in compact spaces. (English) |
| Keyword:
|
weak reflection |
| Keyword:
|
Wallman compactification |
| Keyword:
|
filter (base) |
| Keyword:
|
net |
| Keyword:
|
$\theta$-regul\-arity, weak $\left[\omega_1, \infty\right)^r$-refinability |
| MSC:
|
54C20 |
| MSC:
|
54D20 |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 0860.54024 |
| idMR:
|
MR1364494 |
| . |
| Date available:
|
2009-01-08T18:19:57Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118782 |
| . |
| Reference:
|
[1] Adámek J., Rosický J.: On injectivity in locally presentable categories.preprint, 1991 {published}: Trans. Amer. Math. Soc. 336,2 (1993), 785-804. MR 1085935 |
| Reference:
|
[2] Burke D.K.: Covering properties.Handbook of Set-theoretic Topology K. Kunen and J.E. Vaughan North-Holland Amsterdam (1984), 347-421. Zbl 0569.54022, MR 0776628 |
| Reference:
|
[3] Császár A.: General Topology.Akademiai Kiadó Budapest (1978). |
| Reference:
|
[4] Hušek M.: Čech-Stone-like compactifications for general topological spaces.Comment. Math. Univ. Carolinae 33,1 (1992), 159-163. MR 1173757 |
| Reference:
|
[5] Janković D.S.: $\theta$-regular spaces.preprint {published}: Internat. J. Math. Sci. 8 (1985), no.3, 615-619. MR 0809083 |
| Reference:
|
[6] Kovár M.M.: On $\theta$-regular spaces.Internat. J. Math. Sci. 17 (1994), no. 4, 687-692. MR 1298791 |
| Reference:
|
[7] Kovár M.M.: Product spaces, paracompactness and Boyte's covering property.preprint, 1994. |
| . |
