| Title:
|
Non-normality points and nice spaces (English) |
| Author:
|
Logunov, Sergei |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
383-392 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
J. Terasawa in "$\beta X-\{p\}$ are non-normal for non-discrete spaces $X$" (2007) and the author in "On non-normality points and metrizable crowded spaces" (2007), independently showed for any metrizable crowded space $X$ that each point $p$ of its Čech--Stone remainder $X^{*}$ is a non-normality point of $\beta X$. We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space. (English) |
| Keyword:
|
non-normality point |
| Keyword:
|
butterfly-point |
| Keyword:
|
nice family |
| Keyword:
|
nice space |
| Keyword:
|
metrizable crowded space |
| Keyword:
|
Sorgenfrey line |
| MSC:
|
54D15 |
| MSC:
|
54D35 |
| MSC:
|
54D40 |
| MSC:
|
54D80 |
| MSC:
|
54E35 |
| MSC:
|
54G20 |
| idMR:
|
MR4331289 |
| DOI:
|
10.14712/1213-7243.2021.019 |
| . |
| Date available:
|
2021-10-20T09:24:11Z |
| Last updated:
|
2023-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149147 |
| . |
| Reference:
|
[1] Błaszczyk A., Szymański A.: Some non-normal subspaces of the Čech–Stone compactification of a discrete space.in Abstracta, 8th Winter School on Abstract Analysis, Czechoslovak Academy of Sciences, Praha, 1980, pages 35–38. |
| Reference:
|
[2] Logunov S.: On hereditary normality of compactifications.Topology Appl. 73 (1996), no. 3, 213–216. 10.1016/S0166-8641(96)00063-6 |
| Reference:
|
[3] Logunov S.: On hereditary normality of zero-dimensional spaces.Topology Appl. 102 (2000), no. 1, 53–58. 10.1016/S0166-8641(98)00137-0 |
| Reference:
|
[4] Logunov S.: On remote points, non-normality and $\pi $-weight $\omega _{1}$.Comment. Math. Univ. Carolin. 42 (2001), no. 2, 379–384. |
| Reference:
|
[5] Logunov S.: On non-normality points and metrizable crowded spaces.Comment. Math. Univ. Carolin. 48 (2007), no. 3, 523–527. |
| Reference:
|
[6] Logunov S.: Non-normality points and big products of metrizable spaces.Topology Proc. 46 (2015), 73–85. |
| Reference:
|
[7] Šapirovskiĭ B. È.: The embedding of extremely disconnected spaces in bicompacta. b-points and weight of point-wise normal spaces.Dokl. Akad. Nauk SSSR 223 (1975), no. 5, 1083–1086 (Russian). |
| Reference:
|
[8] Terasawa J.: $\beta X-\{p\}$ are non-normal for non-discrete spaces $X$.Topology Proc. 31 (2007), no. 1, 309–317. |
| Reference:
|
[9] Warren N. M.: Properties of Stone–Čech compactifications of discrete spaces.Proc. Amer. Math. Soc. 33 (1972), 599–606. |
| . |
