Weak normality properties in $\Psi$-spaces

Sergio A; Garcia-Balan; Paul J. Szeptycki

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arXiv · 2007.05844

Weak normality properties in $\Psi$-spaces

Sergio A·Garcia-Balan·Paul J. Szeptycki

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Abstract

Almost disjoint families of true cardinality $\mathfrak{c}$ are used to produce an example of a mildly-normal not partly-normal $\Psi$-space and a quasi-normal not almost-normal $\Psi$-space. This is related with a problem posed by Lufti Kalantan where he asks whether there exists a mad family so that the related Mr\'owka-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.

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BibTeX RIS

Sergio A, Garcia-Balan, Paul J. Szeptycki. 2020-07-11. Weak normality properties in $\Psi$-spaces. https://arxiv.org/abs/2007.05844

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