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Keywords:
$\alpha$-normal; $\beta$-normal; closed unbounded
$\alpha$-normal; $\beta$-normal; closed unbounded
Summary:
$\alpha$-normality and $\beta$-normality are properties generalizing normality of topological spaces. They consist in separating dense subsets of closed disjoint sets. We construct an example of a Tychonoff $\beta$-normal non-normal space and an example of a Hausdorff $\alpha$-normal non-regular space.
References:
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Ludwig L., Szeptycki P.J.: A consistent example of a $\beta$-normal not normal space. Proceedings of the 2000 Topology and Dynamics Conference (San Antonio, TX), Topology Proc. 25 (2000), 1-4. MR 1875595
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