Displaying similar documents to “Tychonoff products of super second countable and super separable metric spaces”

Countable sums and products of Loeb and selective metric spaces

Horst Herrlich, Kyriakos Keremedis, Eleftherios Tachtsis (2005)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the role that weak forms of the axiom of choice play in countable Tychonoff products, as well as countable disjoint unions, of Loeb and selective metric spaces.

Disasters in metric topology without choice

Eleftherios Tachtsis (2002)

Commentationes Mathematicae Universitatis Carolinae

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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 that X has an open dense subspace which is not paracompact and that in ZF the Principle of Dependent Choice, DC, does not imply .