### On $T_3$--topological space omitting many cardinals

by Shelah. [Sh:606]

Periodica Math. Hungarica, 1999

We prove that for every (infinite cardinal) lambda
there is a T_3-space X with clopen basis, 2^mu points
where mu = 2^lambda, such that every closed subspace of
cardinality <|X| has cardinality < lambda .

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