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Eleftherios Tachtsis ,EI=IJAHI E AJHE? JFCO MEJDKJ ?DE?A

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Eleftherios Tachtsis

Disasters in metric topology without choice

Comment.Math.Univ.Carolinae 43,1 (2002) 165-174.

Abstract: We show that it is consistent with ZF that there is a dense-in-itself compact metric space (X, d) which has the countable chain condition (ccc), but X is neither separable nor second countable. It is also shown thatX has an open dense subspace which is not paracompact and that in ZF the Principle of Dependent Choice, DC, does not imply the disjoint union of metrizable spaces is normal.

Keywords: Axiom of Choice, Axiom of Multiple Choice, Principle of Dependent Choice, Ordering Principle, metric spaces, separable metric spaces, second count- able metric spaces, paracompact spaces, compact T2 spaces, ccc spaces.

AMS Subject Classification: 03E25, 54A35, 54D20, 54E35, 54E45, 54F05

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