Almost-normality of Isbell-Mrówka spaces

Abstract

We explore almost-normality in Isbell-Mrówka spaces and some related concepts. We use forcing to provide an example of an almost-normal not normal almost disjoint family, explore the concept of semi-normality in Isbell-Mrówka spaces, define the concept of strongly $({\aleph }_0,<\mathfrak{c})$-separated almost disjoint families and prove the generic existence of completely separable strongly $({\aleph }_0,<\mathfrak{c})$-almost disjoint families assuming $\mathfrak{s}=\mathfrak{c}$ and $\mathfrak{b}=\mathfrak{c}$. We also provide an example of a Tychonoff almost-normal not normal pseudocompact space which is not countably compact, answering a question from P. Szeptycki and S. Garcia-Balan.

Postprint, accepted in Topology and its Applications

References in corpus (1)

• Weak normality properties in $\Psi$-spaces

Cited by in corpus (1)

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