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arXiv · 2009.10209

Almost-normality of Isbell-Mrówka spaces

Vinicius de Oliveira Rodrigues·Victor dos Santos Ronchim
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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.

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Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim. 2020-12-03. Almost-normality of Isbell-Mrówka spaces. https://doi.org/10.1016/j.topol.2020.107470

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