$\alpha$-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.
@article{119308,
author = {Eva Murtinov\'a},
title = {A $\beta$-normal Tychonoff space which is not normal},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {43},
year = {2002},
pages = {159-164},
zbl = {1090.54016},
mrnumber = {1903315},
language = {en},
url = {http://dml.mathdoc.fr/item/119308}
}
Murtinová, Eva. A $\beta$-normal Tychonoff space which is not normal. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 159-164. http://gdmltest.u-ga.fr/item/119308/
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