| Title:
|
On remote points, non-normality and $\pi$-weight $\omega_1$ (English) |
| Author:
|
Logunov, Sergei |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
379-384 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show, in particular, that every remote point of $X$ is a nonnormality point of $\beta X$ if $X$ is a locally compact Lindelöf separable space without isolated points and $\pi w(X)\leq \omega _{1}$. (English) |
| Keyword:
|
remote point |
| Keyword:
|
butterfly-point |
| Keyword:
|
nonnormality point |
| MSC:
|
54D20 |
| MSC:
|
54D35 |
| MSC:
|
54D40 |
| idZBL:
|
Zbl 1053.54031 |
| idMR:
|
MR1832156 |
| . |
| Date available:
|
2009-01-08T19:10:53Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119252 |
| . |
| Reference:
|
[1] Blaszczyk A., Szymanski A.: Some nonnormal subspaces of the Čech-Stone compactifications of a discrete space.(1980), in: Proc. 8-th Winter School on Abstract Analysis, Prague. |
| Reference:
|
[2] Dow A.: Remote points in spaces with $\pi $-weight $ømega _ 1$.(1984), 124 Fund. Math. MR 0774511 |
| Reference:
|
[3] van Douwen E.K.: Why certain Čech-Stone remainders are not homogeneous.(1979), 41 Colloq. Math. Zbl 0424.54012, MR 0550626 |
| Reference:
|
[4] van Douwen E.K.: Remote points.(1988), 188 Dissert. Math. |
| Reference:
|
[5] Gryzlov A.A.: On the question of hereditary normality of the space $\beta ømega \setminus ømega $.(1982), Topology and Set Theory (Udmurt. Gos. Univ., Izhevsk). MR 0760274 |
| Reference:
|
[6] Logunov S.: On hereditary normality of compactifications.(1996), 73 Topology Appl. Zbl 0869.54029, MR 1419794 |
| Reference:
|
[7] Logunov S.: On hereditary normality of zero-dimensional spaces.(2000), 102 Topology Appl. Zbl 0944.54016, MR 1739263 |
| Reference:
|
[8] van Mill J.: An easy proof that $\beta N \setminus N \setminus \{p\} $ is non-normal.(1984), 2 Ann. Math. Silesianea. |
| Reference:
|
[9] Rajagopalan M.: $\beta N \setminus N \setminus \{p\} $ is not normal.(1972), 36 J. Indian Math. Soc. MR 0321012 |
| Reference:
|
[10] Shapirovskij B.: On embedding extremely disconnected spaces in compact Hausdorff spaces, b-points and weight of pointwise normal spaces.(1987), 223 Dokl. Akad. Nauk SSSR. |
| . |
