Dedekind-Endlichkeit und Wohlordenbarkeit.
Disasters in metric topology without choice
We show that it is consistent with ZF that there is a dense-in-itself compact metric space which has the countable chain condition (ccc), but is neither separable nor second countable. It is also shown that 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.
Distinguishing Lindelöfness and inverse Lindelöfness
On a Hausdorff inverse Lindelöf non Lindelöf topology has been constructed.