### On a problem of Juh\'asz and Van Mill

by Shelah and Tsaban. [ShTb:921]

Topology Proc, 2010

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 emph {regular} is weakened to emph {Hausdorff}, and
emph {coutnably compact} is strengthened to
emph {sequentially compact}.

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