On nowhere dense closed 𝑃-sets

Kunen, Kenneth; van Mill, Jan; Mills, Charles F.

doi:10.1090/S0002-9939-1980-0548097-X

On nowhere dense closed $P$-sets
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by Kenneth Kunen, Jan van Mill and Charles F. Mills

Proc. Amer. Math. Soc. 78 (1980), 119-123

DOI: https://doi.org/10.1090/S0002-9939-1980-0548097-X

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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.

References

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