Countable compact Hausdorff spaces need not be metrizable in ZF

Keremedis, Kyriakos; Tachtsis, Eleftherios

doi:10.1090/S0002-9939-06-08572-8

Countable compact Hausdorff spaces need not be metrizable in ZF
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by Kyriakos Keremedis and Eleftherios Tachtsis PDF

Proc. Amer. Math. Soc. 135 (2007), 1205-1211 Request permission

Abstract:

We show that the existence of a countable, first countable, zero-dimensional, compact Hausdorff space which is not second countable, hence not metrizable, is consistent with ZF.

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