Weak 𝑃-points in compact CCC 𝐹-spaces

Dow, Alan

doi:10.1090/S0002-9947-1982-0637709-4

Weak $P$-points in compact CCC $F$-spaces
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Trans. Amer. Math. Soc. 269 (1982), 557-565 Request permission

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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