  A 27 years old and still open problem of Juhasz and van Mill asks whether
there exists a cardinal kappa such that every regular dense in itself countably
compact space has a dense in itself subset of cardinality at most kappa. We
give a negative answer for the analogous question where_regular_ is weakened
to_Hausdorff_, and_coutnably compact_ is strengthened to_sequentially compact_.
