Disasters in metric topology without choice
نویسنده
چکیده
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 the disjoint union of metrizable spaces is normal .
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