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Countable compact Hausdorff spaces need not be metrizable in ZF |
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| Authors: | Kyriakos Keremedis Eleftherios Tachtsis |
| Institution: | Department of Mathematics, University of the Aegean, Karlovassi, 83 200, Samos, Greece ; Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, 83 200, Samos, Greece |
| 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. |
| Keywords: | Axiom of choice weak axioms of choice compact spaces Hausdorff spaces countable spaces first countable spaces second countable spaces metrizable spaces zero-dimensional spaces paracompact spaces metacompact spaces |
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