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Weak normality properties in ${\varPsi }$-spaces

Volume 258 / 2022

Sergio A. Garcia-Balan, Paul J. Szeptycki 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.

Authors

  • Sergio A. Garcia-BalanDepartment of Mathematics and Statistics
    York University
    4700 Keele St.
    Toronto, ON M3J 1P3, Canada
    e-mail
  • Paul J. SzeptyckiDepartment of Mathematics and Statistics
    York University
    4700 Keele St.
    Toronto, ON M3J 1P3. Canada
    e-mail

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