Small MAD families whose Isbell--Mr\'owka space has pseudocompact hyperspace
Volume 247 / 2019
Fundamenta Mathematicae 247 (2019), 99-108
MSC: Primary 54B20, 54D80; Secondary 54D20, 54A35.
DOI: 10.4064/fm657-10-2018
Published online: 30 May 2019
Abstract
We prove that it is consistent that there exists a MAD family $\mathcal A$ of cardinality $\omega _1 \lt \mathfrak c$ such that the Vietoris hyperspace of its Isbell–Mrówka space, ${\rm CL} (\varPsi (\mathcal A))$, is pseudocompact. In the same model, there exist MAD families $\mathcal A_1, \mathcal A_2$ such that ${\rm CL} (\varPsi (\mathcal A_1))$ is pseudocompact but ${\rm CL} (\varPsi (\mathcal A_2))$ is not.
