Weak 𝑃-points in Čech-Stone compactifications

van Mill, Jan

doi:10.1090/S0002-9947-1982-0667166-3

Weak $P$-points in Čech-Stone compactifications
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by Jan van Mill

Trans. Amer. Math. Soc. 273 (1982), 657-678

DOI: https://doi.org/10.1090/S0002-9947-1982-0667166-3

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Abstract:

Let $X$ be a nonpseudocompact space which is either nowhere ccc or nowhere of weight $\leqslant {2^\omega }$. Then $\beta X - X$ contains a point $x$ which is a weak $P$-point of $\beta X$, i.e. if $F \subset \beta X - \{ x\}$ is countable, then $x \notin \bar F$. In addition, under MA, if $X$ is any nonpseudocompact space, then $\beta X - X$ contains a point $x$ such that whenever $F \subset \beta X - \{ x\}$ is countable and nowhere dense, then $x \notin \bar F$.

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