| Title:
|
A $\beta$-normal Tychonoff space which is not normal (English) |
| Author:
|
Murtinová, Eva |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
159-164 |
| . |
| Category:
|
math |
| . |
| Summary:
|
$\alpha$-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. (English) |
| Keyword:
|
$\alpha$-normal |
| Keyword:
|
$\beta$-normal |
| Keyword:
|
closed unbounded |
| MSC:
|
03E75 |
| MSC:
|
54A05 |
| MSC:
|
54D15 |
| idZBL:
|
Zbl 1090.54016 |
| idMR:
|
MR1903315 |
| . |
| Date available:
|
2009-01-08T19:20:33Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119308 |
| . |
| Reference:
|
[AL] Arhangel'skii A. V., Ludwig L.: On $\alpha$-normal and $\beta$-normal spaces.Comment. Math. Univ. Carolinae 42.3 (2001), 507-519. Zbl 1053.54030, MR 1860239 |
| Reference:
|
[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 |
| Reference:
|
[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. Zbl 0286.54008, MR 0413044 |
| Reference:
|
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 |
| . |
