Abstract:$\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.
Keywords: $\alpha $-normal, $\beta $-normal, closed unbounded
AMS Subject Classification: 54A05, 54D15, 03E75