Displaying similar documents to “On some properties of Hurewicz, Menger, and Rothberger”

Disasters in metric topology without choice

Eleftherios Tachtsis (2002)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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 .