| Title:
|
Connected Hausdorff subtopologies (English) |
| Author:
|
Porter, Jack |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
195-201 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825--841]. A non-H-closed, Hausdorff space with countable $\pi $-weight and no connected, Hausdorff subtopology is provided. (English) |
| Keyword:
|
connected |
| Keyword:
|
H-closed |
| Keyword:
|
extensions |
| Keyword:
|
condensations |
| MSC:
|
54A10 |
| MSC:
|
54C10 |
| MSC:
|
54D05 |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 1053.54002 |
| idMR:
|
MR1825383 |
| . |
| Date available:
|
2009-01-08T19:09:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119234 |
| . |
| Reference:
|
[PT] Porter J.R., Tikoo M.L.: On Katětov spaces.Trans. Amer. Math. Soc. 289 (4) (1985), 59-71. MR 0779052 |
| Reference:
|
[PV] Porter J.R., Vermeer J.: Space with coarser minimal Hausdorff topologies.Canad. Math. Bull. 32.4 (1989), 425-433. |
| Reference:
|
[PW1] Porter J.R., Woods R.G.: Extensions and Absolutes of Hausdorff Spaces.Springer-Verlag, Berlin, 1988. Zbl 0652.54016, MR 0918341 |
| Reference:
|
[PW2] Porter J.R., Woods R.G.: Subspaces of connected spaces.Topology Appl. 68 (1996), 113-131. Zbl 0855.54025, MR 1374077 |
| Reference:
|
[V] Vermeer J.: Private communication, 1984.. |
| Reference:
|
[TTUW] Tkačenko M.G., Tkachuk V.V., Uspenskij V.V., Wilson R.G.: In quest of weaker connected topologies.Comment. Math Univ. Carolinae 37.4 (1996), 825-841. MR 1440714 |
| . |
