| Title:
|
On pseudocompactness and related notions in ZF (English) |
| Author:
|
Keremedis, Kyriakos |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
371-381 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study in ZF and in the class of $T_{1}$ spaces the web of implications/ non-implications between the notions of pseudocompactness, light compactness, countable compactness and some of their ZFC equivalents. (English) |
| Keyword:
|
axiom of choice |
| Keyword:
|
countably compact |
| Keyword:
|
lightly compact topological space |
| Keyword:
|
pseudocompact topological space |
| MSC:
|
03E25 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 06940877 |
| idMR:
|
MR3861559 |
| DOI:
|
10.14712/1213-7243.2015.256 |
| . |
| Date available:
|
2018-09-10T12:16:38Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147404 |
| . |
| Reference:
|
[1] Dow A., Porter J. R., Stephenson Jr. R. M., Woods R. G.: Spaces whose pseudocompact subspaces are closed subsets.Appl. Gen. Topol. 5 (2004), no. 2, 243–264. Zbl 1066.54024, MR 2121792, 10.4995/agt.2004.1973 |
| Reference:
|
[2] Hewitt E.: Rings of real-valued continuous functions I.Trans. Amer. Math. Soc. 64 (1948), 45–99. Zbl 0032.28603, MR 0026239, 10.1090/S0002-9947-1948-0026239-9 |
| Reference:
|
[3] Howard P., Rubin J. E.: Consequences of the Axiom of Choice.Mathematical Surveys and Monographs, 59, American Mathematical Society, Providence, 1998. Zbl 0947.03001, MR 1637107, 10.1090/surv/059 |
| Reference:
|
[4] Keremedis K.: On lightly and countably compact spaces in $ ZF$.published online in Quaest. Math. (2018), 14 pages. |
| Reference:
|
[5] Mardešić S., Papić P.: Sur les espaces dont toute transformation réelle continue est bornée.Hrvatsko Prirod. Društvo. Glasnik Mat.-Fiz. Astr. Ser. II. 10 (1955), 225–232 (French. Serbo-Croatian summary). MR 0080292 |
| Reference:
|
[6] Scott B. M.: Pseudocompact, metacompact spaces are compact.The Proc. of the 1979 Topology Conf., Ohio Univ., Athens, Ohio, 1979, Topology Proc. 4 (1979), no. 2, 577–587. MR 0598295 |
| Reference:
|
[7] Stone A. H.: Hereditarily compact spaces.Amer. J. Math. 82 (1960), 900–916. MR 0120620, 10.2307/2372948 |
| Reference:
|
[8] Watson W. S.: Pseudocompact metacompact spaces are compact.Proc. Amer. Math. Soc. 81 (1981), no. 1, 151–152. MR 0589159 |
| . |
