| Title:
|
On Szymański theorem on hereditary normality of $\beta\omega$ (English) |
| Author:
|
Logunov, Sergei |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
63 |
| Issue:
|
4 |
| Year:
|
2022 |
| Pages:
|
507-512 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss the following result of A. Szymański in ``Retracts and non-normality points" (2012), Corollary 3.5.: If $F$ is a closed subspace of $\omega ^{*}$ and the $\pi$-weight of $F$ is countable, then every nonisolated point of $F$ is a non-normality point of $\omega ^{*}$. We obtain stronger results for all types of points, excluding the limits of countable discrete sets considered in ``Some non-normal subspaces of the Čech--Stone compactification of a discrete space'' (1980) by A. Błaszczyk and A. Szymański. Perhaps our proofs look ``more natural in this area''. (English) |
| Keyword:
|
Čech--Stone compactification |
| Keyword:
|
non-normality point |
| Keyword:
|
butterfly-point |
| Keyword:
|
countable $\pi$-weight |
| MSC:
|
54D15 |
| MSC:
|
54D35 |
| MSC:
|
54D40 |
| MSC:
|
54D80 |
| MSC:
|
54E35 |
| MSC:
|
54G20 |
| idZBL:
|
Zbl 07729556 |
| idMR:
|
MR4577044 |
| DOI:
|
10.14712/1213-7243.2023.011 |
| . |
| Date available:
|
2023-04-20T13:56:06Z |
| Last updated:
|
2025-01-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151649 |
| . |
| Reference:
|
[1] Bešlagić A., van Douwen E. K.: Spaces of nonuniform ultrafilters in spaces of uniform ultrafilters.Topology Appl. 35 (1990), no. 2–3, 253–260. MR 1058805, 10.1016/0166-8641(90)90110-N |
| Reference:
|
[2] Błaszczyk A., Szymański A.: Some non-normal subspaces of the Čech–Stone compactification of a discrete space.Abstracta, 8th Winter School on Abstract Analysis, Praha, Czechoslovak Academy of Sciences, 1980, 35–38. |
| Reference:
|
[3] Gryzlov A. A.: On the question of hereditary normality of the space $\beta \omega \setminus \omega$.Topology and Set Theory Udmurt. Gos. Univ. Izhevsk (1982), 61–64 (Russian). MR 0760274 |
| Reference:
|
[4] Logunov S.: On non-normality points and metrizable crowded spaces.Comment. Math. Univ. Carolin. 48 (2007), no. 3, 523–527. MR 2374131 |
| Reference:
|
[5] Rajagopalan M.: $\beta N-N-\{p\}$ is not normal.J. Indian Math. Soc. (N.S.) 36 (1972), 173–176. MR 0321012 |
| Reference:
|
[6] Shapirovkij B.: On embedding extremely disconnected spaces in compact Hausdorff spaces, $b$-points and weight of point-wise normal spaces.Dokl. Akad. Nauk SSSR 223 (1975), 1083–1086 (Russian). MR 0394609 |
| Reference:
|
[7] Szymański A.: Retracts and non-normality points.Topology Proc. 40 (2012), 195–201. MR 2832067 |
| Reference:
|
[8] Warren N. M.: Properties of Stone–Čech compactifications of discrete spaces.Proc. Amer. Math. Soc. 33 (1972), 599–606. MR 0292035 |
| . |
