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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