A regular topological space having no closed subsets of cardinality $\aleph_ 2$

by Goldstern and Judah and Shelah. [GJSh:369]
Proc American Math Soc, 1991
We show in ZFC that there is a regular (even zerodimensional) topological space of size > aleph_2 in which there are no closed sets of size aleph_2 . The proof starts by noticing that if beta omega does not work, then we can use a diamondsuit .


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