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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Weak $ P$-points in Čech-Stone compactifications


Author: Jan van Mill
Journal: Trans. Amer. Math. Soc. 273 (1982), 657-678
MSC: Primary 54D35; Secondary 54D40
MathSciNet review: 667166
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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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DOI: https://doi.org/10.1090/S0002-9947-1982-0667166-3
Keywords: Čech-Stone compactification, weak $ P$-point, homogeneous
Article copyright: © Copyright 1982 American Mathematical Society