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 (ℵ0,<c)-separated almost disjoint families and prove the generic existence of completely separable strongly (ℵ0,<c)-separated almost disjoint families assuming s=c and b=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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