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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On nowhere dense closed $ P$-sets


Authors: Kenneth Kunen, Jan van Mill and Charles F. Mills
Journal: Proc. Amer. Math. Soc. 78 (1980), 119-123
MSC: Primary 54D25; Secondary 54A25
MathSciNet review: 548097
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Abstract: We show that no compact space of weight $ {\omega _1}$ can be covered by nowhere dense closed P-sets. In addition, we construct a compact space of weight $ {\omega _2}$ which can be covered by nowhere dense closed P-sets. As an application, we show that CH is equivalent to the statement that each small nonpseudocompact space has a remote point.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0548097-X
Keywords: Nowhere dense, P-set, remote point, CH
Article copyright: © Copyright 1980 American Mathematical Society