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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Countable compact Hausdorff spaces need not be metrizable in ZF


Authors: Kyriakos Keremedis and Eleftherios Tachtsis
Journal: Proc. Amer. Math. Soc. 135 (2007), 1205-1211
MSC (2000): Primary 03E25, 03E35, 54A35, 54D10, 54D30, 54D35, 54D65, 54D70, 54E35.
Published electronically: October 4, 2006
MathSciNet review: 2262927
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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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Additional Information

Kyriakos Keremedis
Affiliation: Department of Mathematics, University of the Aegean, Karlovassi, 83 200, Samos, Greece
Email: kker@aegean.gr

Eleftherios Tachtsis
Affiliation: Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, 83 200, Samos, Greece
Email: ltah@aegean.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08572-8
PII: S 0002-9939(06)08572-8
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.
Received by editor(s): March 18, 2005
Received by editor(s) in revised form: May 15, 2005, November 5, 2005, and November 10, 2005
Published electronically: October 4, 2006
Communicated by: Julia Knight
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.