# Article

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Keywords:
$p$-pseudocompactness; ultrapseudocompactness; strongly pseudocompactness; strongly $p$-pseudocompactness; weak $P$-points; $\mathfrak{c}$-OK points
Summary:
Let $W$ be the subspace of $\mathbb N^*$ consisting of all weak $P$-points. It is not hard to see that $W$ is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that $W$ is a $p$-pseudocompact space for all $p \in \mathbb N^*$.
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