| Title:
|
The Rothberger property on $C_p(\Psi(\mathcal A),2)$ (English) |
| Author:
|
Bernal-Santos, Daniel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
83-88 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A space $X$ is said to have the Rothberger property (or simply $X$ is Rothberger) if for every sequence $\langle\,\mathcal U_n:n\in \omega\,\rangle$ of open covers of $X$, there exists $U_n\in \mathcal U_n$ for each $n\in\omega$ such that $X = \bigcup_{n\in \omega}U_n$. For any $n\in \omega$, necessary and sufficient conditions are obtained for $C_p(\Psi(\mathcal A),2)^n$ to have the Rothberger property when $\mathcal A$ is a Mrówka mad family and, assuming CH (the Continuum Hypothesis), we prove the existence of a maximal almost disjoint family $\mathcal A$ for which the space $C_p(\Psi(\mathcal A),2)^n\,$ is Rothberger for all $n\in\omega$. (English) |
| Keyword:
|
function spaces |
| Keyword:
|
$C_p(X,Y)$ |
| Keyword:
|
Rothberger spaces |
| Keyword:
|
$\Psi$-space |
| MSC:
|
03G10 |
| MSC:
|
54C35 |
| MSC:
|
54C45 |
| MSC:
|
54D35 |
| MSC:
|
54D45 |
| idZBL:
|
Zbl 06562198 |
| idMR:
|
MR3478341 |
| DOI:
|
10.14712/1213-7243.2015.145 |
| . |
| Date available:
|
2016-04-12T05:05:38Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144917 |
| . |
| Reference:
|
[1] Arhangel'skiĭ A.V.: Topological Function Spaces.Mathematics and its Applications (Soviet Series), Kluwer Academic Publishers, 1992. MR 1144519 |
| Reference:
|
[2] Bernal-Santos D.: The Rothberger property on $C_p(X, 2)$.Topology Appl. 196 (2015), 106–119. MR 3422736 |
| Reference:
|
[3] Bernal-Santos D., Tamariz-Macarúa Á.: The Menger property on $C_p(X,2)$.Topology Appl. 183 (2015), 110–126. MR 3310340 |
| Reference:
|
[4] Hurewicz W.: Über eine Verallgemeinerung des Borelschen Theorems.Math. Z. 24 (1926), 401–421. MR 1544773, 10.1007/BF01216792 |
| Reference:
|
[5] Just W., Miller W., Scheepers M., Szeptycki J.: The combinatorics of open covers II.Topology Appl. 73 (1996), 241–266. MR 1419798, 10.1016/S0166-8641(96)00075-2 |
| Reference:
|
[6] Hrušák M., Szeptycki P.J., Tamariz-Mascarúa Á.: Spaces of functions defined on Mrówka spaces.Topology Appl. 148 (2005), no. (1-3), 239–252. MR 2118968, 10.1016/j.topol.2004.09.009 |
| Reference:
|
[7] Rothberger F.: Eine Verschärfung der Eigenschaft C.Fund. Math. 30 (1938), 50–55. |
| . |
