论文标题
最大的几乎不连接家族和超空间的假发性
Maximal almost disjoint families and pseudocompactness of hyperspaces
论文作者
论文摘要
我们表明，当且仅当$ \ mathsf {ma} _ \ Mathfrak C（\ Mathcal P（ω）/\ Mathrm {Finrm {Fin}）$时，所有最大几乎几乎不相交的家族都有假发越越野空间。 We further study the question whether there is a maximal almost disjoint family whose hyperspace is pseudocompact and prove that consistently such families do not exist \emph{genericaly}, by constructing a consistent example of a maximal almost disjoint family $\mathcal A$ of size less than $\mathfrak c$ whose hyperspace is not pseudocompact.
We show that all maximal almost disjoint families have pseudocompact Vietoris hyperspace if and only if $\mathsf{MA}_\mathfrak c (\mathcal P(ω)/\mathrm{fin})$ holds. We further study the question whether there is a maximal almost disjoint family whose hyperspace is pseudocompact and prove that consistently such families do not exist \emph{genericaly}, by constructing a consistent example of a maximal almost disjoint family $\mathcal A$ of size less than $\mathfrak c$ whose hyperspace is not pseudocompact.
