# A $\beta $-normal Tychonoff space which is not normal

Commentationes Mathematicae Universitatis Carolinae (2002)

- Volume: 43, Issue: 1, page 159-164
- ISSN: 0010-2628

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topMurtinová, Eva. "A $\beta $-normal Tychonoff space which is not normal." Commentationes Mathematicae Universitatis Carolinae 43.1 (2002): 159-164. <http://eudml.org/doc/248954>.

@article{Murtinová2002,

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.},

author = {Murtinová, Eva},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {$\alpha $-normal; $\beta $-normal; closed unbounded; generalized normal space},

language = {eng},

number = {1},

pages = {159-164},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A $\beta $-normal Tychonoff space which is not normal},

url = {http://eudml.org/doc/248954},

volume = {43},

year = {2002},

}

TY - JOUR

AU - Murtinová, Eva

TI - A $\beta $-normal Tychonoff space which is not normal

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2002

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 43

IS - 1

SP - 159

EP - 164

AB - $\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.

LA - eng

KW - $\alpha $-normal; $\beta $-normal; closed unbounded; generalized normal space

UR - http://eudml.org/doc/248954

ER -

## References

top- Arhangel'skii A. V., Ludwig L., On $\alpha $-normal and $\beta $-normal spaces, Comment. Math. Univ. Carolinae 42.3 (2001), 507-519. (2001) Zbl1053.54030MR1860239
- Balcar B., Simon P., Disjoint refinement, Handbook of Boolean Algebras J.D. Monk, R. Bonnet Elsevier Science Publishers B.V. (1989), 333-386. (1989) MR0991597
- 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. (1974) Zbl0286.54008MR0413044
- 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. (2000) MR1875595

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