| Title:
|
AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology (English) |
| Author:
|
Herrlich, Horst |
| Author:
|
Keremedis, Kyriakos |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
139-143 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology. (English) |
| Keyword:
|
axiom of choice |
| Keyword:
|
compactness |
| MSC:
|
03E25 |
| MSC:
|
54A10 |
| MSC:
|
54C45 |
| MSC:
|
54G20 |
| idZBL:
|
Zbl 1240.54081 |
| idMR:
|
MR2828364 |
| . |
| Date available:
|
2011-03-08T17:43:44Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141433 |
| . |
| Reference:
|
[1] Herrlich H.: An Effective Construction of a Free z-ultrafilter.Ann. New York Acad. Sci., 806 (1996), 201–206. Zbl 0882.54023, MR 1429654, 10.1111/j.1749-6632.1996.tb49169.x |
| Reference:
|
[2] Herrlich H., Keremedis K.: Extending compact topologies to compact Hausdorff topologies in ZF., submitted manuscript. |
| Reference:
|
[3] Howard P., Rubin J.E.: Consequences of the Axiom of Choice.Mathematical Surveys and Monographs, 59, American Mathematical Society, Providence, RI, 1998. Zbl 0947.03001, MR 1637107 |
| Reference:
|
[4] Keremedis K.: The compactness of $ 2^{\mathbb{R}}$ and some weak forms of the axiom of choice.MLQ Math. Log. Q. {bf 46} (2000), no. 4, 569–571. Zbl 0963.03071, MR 1791873 |
| . |
