| Title:
|
A note on spaces with countable extent (English) |
| Author:
|
Song, Yan-Kui |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
397-399 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $P$ be a topological property. A space $X$ is said to be star P if whenever $\mathcal U$ is an open cover of $X$, there exists a subspace $A\subseteq X$ with property $P$ such that $X=St(A,\mathcal U)$. In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa. (English) |
| Keyword:
|
star properties |
| Keyword:
|
star Lindelöf |
| Keyword:
|
space with star countable extent |
| MSC:
|
54B05 |
| MSC:
|
54B10 |
| MSC:
|
54C10 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 06837074 |
| idMR:
|
MR3708782 |
| DOI:
|
10.14712/1213-7243.2015.211 |
| . |
| Date available:
|
2017-11-22T09:27:26Z |
| Last updated:
|
2019-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146912 |
| . |
| Reference:
|
[1] Aiken L.P.: Star-covering properties: generalized $\Psi$-spaces, countability conditions, reflection.Topology Appl. 158 (2011), 1732–1737. Zbl 1223.54029, MR 2812483, 10.1016/j.topol.2011.06.032 |
| Reference:
|
[2] Alas O.T., Junqueira L.R., Wilson R.G.: Countability and star covering properties.Topology Appl. 158 (2011), 620–626. Zbl 1226.54023, MR 2765618, 10.1016/j.topol.2010.12.012 |
| Reference:
|
[3] Alas O.T., Junqueira L.R., van Mill J., Tkachuk V.V., Wilson R.G.: On the extent of star countable spaces.Cent. Eur. J. Math. 9 (2011), no 3, 603–615. Zbl 1246.54017, MR 2784032, 10.2478/s11533-011-0018-y |
| Reference:
|
[4] van Douwen E.K., Reed G.M., Roscoe A.W., Tree I.J.: Star covering properties.Topology Appl. 39 (1991), 71–103. Zbl 0743.54007, MR 1103993, 10.1016/0166-8641(91)90077-Y |
| Reference:
|
[5] Engelking R.: General Topology.revised and completed edition, Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[6] Matveev M.V.: A survey on star-covering properties.Topological Atlas preprint no. 330, 1998. |
| Reference:
|
[7] van Mill J., Tkachuk V.V., Wilson R.G.: Classes defined by stars and neighborhood assignments.Topology Appl. 154 (2007), 2127–2134. MR 2324924, 10.1016/j.topol.2006.03.029 |
| Reference:
|
[8] Noble N.: Countably compact and pseudocompact products.Czechoslovak Math. J. 19(3) (1969), 390–397. Zbl 0184.47706, MR 0248717 |
| Reference:
|
[9] Rojas-Sánchez A.D., Tamariz-Mascarúa Á.: Spaces with star countable extent.Comment. Math. Univ. Carolin. 57 (2016), no 3, 381–395. MR 3554518 |
| . |
