| Title:
|
Aull-paracompactness and strong star-normality of subspaces in topological spaces (English) |
| Author:
|
Yamazaki, Kaori |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
743-747 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove for a subspace $Y$ of a $T_1$-space $X$, $Y$ is (strictly) Aull-paracompact in $X$ and $Y$ is Hausdorff in $X$ if and only if $Y$ is strongly star-normal in $X$. This result provides affirmative answers to questions of A.V. Arhangel'skii–I.Ju. Gordienko [3] and of A.V. Arhangel'skii [2]. (English) |
| Keyword:
|
Aull-paracompactness of $Y$ in $X$ |
| Keyword:
|
strong star-normality of $Y$ in $X$ |
| MSC:
|
54B05 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 1099.54023 |
| idMR:
|
MR2103089 |
| . |
| Date available:
|
2009-05-05T16:48:53Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119499 |
| . |
| Reference:
|
[1] Arhangel'skii A.V.: Relative topological properties and relative topological spaces.Topology Appl. 70 (1996), 87-99. Zbl 0848.54016, MR 1397067 |
| Reference:
|
[2] Arhangel'skii A.V.: From classic topological invariants to relative topological properties.Sci. Math. Japon. 55 (2002), 153-201. MR 1885790 |
| Reference:
|
[3] Arhangel'skii A.V., Gordienko I.Ju.: Relative symmetrizability and metrizability.Comment. Math. Univ. Carolinae 37 (1996), 757-774. Zbl 0886.54001, MR 1440706 |
| Reference:
|
[4] Burke D.K.: Covering properties.in: K. Kunen, J.E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp.347-422. Zbl 0569.54022, MR 0776628 |
| Reference:
|
[5] Engelking R.: General Topology.Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[6] Hoshina T., Yamazaki K.: Weak $C$-embedding and $P$-embedding, and product spaces.Topology Appl. 125 (2002), 233-247. Zbl 1013.54006, MR 1933574 |
| Reference:
|
[7] Yamazaki K.: Absolute weak $C$-embedding in Hausdorff spaces.Topology Appl. 131 (2003), 273-279. Zbl 1025.54010, MR 1983083 |
| . |
