AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology
Horst Herrlich; Kyriakos Keremedis
Commentationes Mathematicae Universitatis Carolinae (2011)
- Volume: 52, Issue: 1, page 139-143
- ISSN: 0010-2628
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topHerrlich, Horst, and Keremedis, Kyriakos. "AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology." Commentationes Mathematicae Universitatis Carolinae 52.1 (2011): 139-143. <http://eudml.org/doc/246433>.
@article{Herrlich2011,
abstract = {We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.},
author = {Herrlich, Horst, Keremedis, Kyriakos},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {axiom of choice; compactness; axiom of choice; compactness},
language = {eng},
number = {1},
pages = {139-143},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology},
url = {http://eudml.org/doc/246433},
volume = {52},
year = {2011},
}
TY - JOUR
AU - Herrlich, Horst
AU - Keremedis, Kyriakos
TI - AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 1
SP - 139
EP - 143
AB - We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.
LA - eng
KW - axiom of choice; compactness; axiom of choice; compactness
UR - http://eudml.org/doc/246433
ER -
References
top- Herrlich H., 10.1111/j.1749-6632.1996.tb49169.x, Ann. New York Acad. Sci., 806 (1996), 201–206. Zbl0882.54023MR1429654DOI10.1111/j.1749-6632.1996.tb49169.x
- Herrlich H., Keremedis K., Extending compact topologies to compact Hausdorff topologies in ZF, , submitted manuscript.
- Howard P., Rubin J.E., Consequences of the Axiom of Choice, Mathematical Surveys and Monographs, 59, American Mathematical Society, Providence, RI, 1998. Zbl0947.03001MR1637107
- Keremedis K., The compactness of and some weak forms of the axiom of choice, MLQ Math. Log. Q. {bf 46} (2000), no. 4, 569–571. Zbl0963.03071MR1791873
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