Previous |  Up |  Next


$\alpha$-normal; $\beta$-normal; closed unbounded
$\alpha$-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.
[AL] Arhangel'skii A. V., Ludwig L.: On $\alpha$-normal and $\beta$-normal spaces. Comment. Math. Univ. Carolinae 42.3 (2001), 507-519. MR 1860239 | Zbl 1053.54030
[BS] Balcar B., Simon P.: Disjoint refinement. Handbook of Boolean Algebras J.D. Monk, R. Bonnet Elsevier Science Publishers B.V. (1989), 333-386. MR 0991597
[Jo] Jones F.B.: Hereditarily separable, non-completely regular spaces. Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, VA, 1973) Lecture Notes in Math., vol. 375, Springer, Berlin (1974), 149-152. MR 0413044 | Zbl 0286.54008
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
Partner of
EuDML logo