Accumulation points of nowhere dense sets in 𝐻-closed spaces

Porter, Jack R.; Woods, R. Grant

doi:10.1090/S0002-9939-1985-0774019-7

Accumulation points of nowhere dense sets in $H$-closed spaces
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by Jack R. Porter and R. Grant Woods PDF

Proc. Amer. Math. Soc. 93 (1985), 539-542 Request permission

Abstract:

In this paper a ten year old problem by Kulpa and Szymański is settled by constructing an example of a minimal Hausdorff space without isolated points which has a point that is not the accumulation point of any nowhere dense subset of the minimal Hausdorff space. Also, a result by Kulpa and Szymański is extended by showing that a regular point in an $H$-closed space without isolated points is the accumulation point of some nowhere dense subset.

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When all semiregular

-closed extensions are compact

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