Weak normality properties in ${\varPsi }$-spaces
Volume 258 / 2022
Fundamenta Mathematicae 258 (2022), 137-151
MSC: Primary 54D15; Secondary 54G20.
DOI: 10.4064/fm935-11-2021
Published online: 11 April 2022
Abstract
Almost disjoint families of true cardinality $\mathfrak c$ are used to produce an example of a mildly-normal non-partly-normal $\Psi $-space and a quasi-normal non-almost-normal $\Psi $-space. This is related to a problem, posed by Kalantan (2017), whether there exists a mad family such that the related Mrówka–Isbell space is partly-normal. In addition, a consistent example of a Luzin mad family such that its associated $\Psi $-space is quasi-normal is provided.
