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Article

Herrlich, Horst ; Keremedis, Kyriakos
AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 52 (2011), issue 1, pp. 139-143
MSC: 03E25, 54A10, 54C45, 54G20 | MR 2828364 | Zbl 1240.54081
Keywords:
axiom of choice; compactness
Summary:
We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.
References:
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[2] Herrlich H., Keremedis K.: Extending compact topologies to compact Hausdorff topologies in ZF. submitted manuscript.
[3] Howard P., Rubin J.E.: Consequences of the Axiom of Choice. Mathematical Surveys and Monographs, 59, American Mathematical Society, Providence, RI, 1998. MR 1637107 | Zbl 0947.03001
[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. MR 1791873 | Zbl 0963.03071
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