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Transactions of the American Mathematical Society

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

 

 

Weak $ P$-points in compact CCC $ F$-spaces


Author: Alan Dow
Journal: Trans. Amer. Math. Soc. 269 (1982), 557-565
MSC: Primary 54D35; Secondary 03E50
MathSciNet review: 637709
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Abstract: Using a technique due to van Mill we show that each compact ccc $ F$-space of weight greater than $ {2^\omega }$ contains a weak $ P$-point, i.e. a point $ x \in X$ such that $ x \notin \overline F $ for each countable $ F \subset X - \{ x\} $. We show that, assuming $ BF(c)$, each nowhere separable compact $ F$-space has a weak $ P$-point. We show the existence of points which are not limit points of any countable nowhere dense set in compact $ F$-spaces of weight $ {\aleph _1}$. We also discuss remote points and points not the limit point of any countable discrete set.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0637709-4
Keywords: Weak $ P$-point, $ F$-space, ccc
Article copyright: © Copyright 1982 American Mathematical Society