Geodesic
A $\beta$-normal Tychonoff space which is not normal
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 1, pp. 159-164.

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$\alpha$-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.
Classification : 03E75, 54A05, 54D15
Keywords: $\alpha$-normal; $\beta$-normal; closed unbounded 
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     title = {A $\beta$-normal {Tychonoff} space which is not normal},
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Murtinová, Eva. A $\beta$-normal Tychonoff space which is not normal. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 1, pp. 159-164. http://geodesic.mathdoc.fr/item/CMUC_2002__43_1_a13/