Geodesic
AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 139-143.

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We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.
Classification : 03E25, 54A10, 54C45, 54G20
Keywords: axiom of choice; compactness 
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Herrlich, Horst; Keremedis, Kyriakos. AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 139-143. http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a9/