Weak 𝑃-points in Čech-Stone compactifications

van Mill, Jan

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

Weak -points in Čech-Stone compactifications

Author: Jan van Mill
Journal: Trans. Amer. Math. Soc. 273 (1982), 657-678
MSC: Primary 54D35; Secondary 54D40
DOI: https://doi.org/10.1090/S0002-9947-1982-0667166-3
MathSciNet review: 667166
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Abstract: Let be a nonpseudocompact space which is either nowhere ccc or nowhere of weight $\leqslant {2^\omega }$ . Then $\beta X - X$ contains a point which is a weak -point of $\beta X$ , i.e. if $F \subset \beta X - \{ x\}$ is countable, then $x \notin \bar F$ . In addition, under MA, if is any nonpseudocompact space, then $\beta X - X$ contains a point such that whenever $F \subset \beta X - \{ x\}$ is countable and nowhere dense, then $x \notin \bar F$ .

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