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Countable compact Hausdorff spaces need not be metrizable in ZF
Author(s):
Kyriakos
Keremedis;
Eleftherios
Tachtsis
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1205-1211.
MSC (2000):
Primary 03E25, 03E35, 54A35, 54D10, 54D30, 54D35, 54D65, 54D70, 54E35.
Posted:
October 4, 2006
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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:
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
Posted:
October 4, 2006
Communicated by:
Julia Knight
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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