publication . Preprint . 2020

Maximal almost disjoint families and pseudocompactness of hyperspaces

Guzmán, Osvaldo; Hrušák, Michael; Rodrigues, Vinicius de Oliveira; Todorčević, Stevo; Tomita, Artur Hideyuki;
Open Access English
  • Published: 18 Apr 2020
Abstract
We show that all maximal almost disjoint families have pseudocompact Vietoris hyperspace if and only if $\mathsf{MA}_\mathfrak c (\mathcal P(\omega)/\mathrm{fin})$ 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.
Subjects
arXiv: Mathematics::General Topology
free text keywords: Mathematics - General Topology, Primary 54D20, 03E35, Secondary 54D35, 03E17
Funded by
NSERC
Project
  • Funder: Natural Sciences and Engineering Research Council of Canada (NSERC)
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