A β -normal Tychonoff space which is not normal

Eva Murtinová

Commentationes Mathematicae Universitatis Carolinae (2002)

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

Abstract

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α -normality and β -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 β -normal non-normal space and an example of a Hausdorff α -normal non-regular space.

How to cite

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Murtinová, 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

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  1. Arhangel'skii A. V., Ludwig L., On α -normal and β -normal spaces, Comment. Math. Univ. Carolinae 42.3 (2001), 507-519. (2001) Zbl1053.54030MR1860239
  2. 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
  3. 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
  4. Ludwig L., Szeptycki P.J., A consistent example of a β -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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