Abstract
In this paper we investigate for nowhere locally compact realcompact spaces X the question when X ∗=βX−X has properties related to being extremally disconnected. We prove that the set of 2-points of X has compact closure in X iff X ∗ is extremally disconnected iff X ∗ is in Oz; if X is in addition in Oz (in particular if X is perfectly normal), then these conditions are equivalent to X ∗ being an F′-space, in particular to X ∗ being an F-space. We also prove that each regularly closed G δ-set of X ∗ is clopen in X ∗. This can be used to find for each n⩾1 a compact space K with dim K = n which has no regularly closed G δ-sets except Ø and K (such K were first constructed by Fedorčuk).
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