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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Accumulation points of nowhere dense sets in $ H$-closed spaces


Authors: Jack R. Porter and R. Grant Woods
Journal: Proc. Amer. Math. Soc. 93 (1985), 539-542
MSC: Primary 54D25
MathSciNet review: 774019
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0774019-7
PII: S 0002-9939(1985)0774019-7
Keywords: Nowhere dense sets, accumulation points, H-closed spaces, minimal Hausdorff spaces
Article copyright: © Copyright 1985 American Mathematical Society