Article
MSC:
03G10,
54C35,
54C45,
54D35,
54D45 | MR 3478341 | Zbl 06562198 | DOI: 10.14712/1213-7243.2015.145
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Keywords:
function spaces; $C_p(X,Y)$; Rothberger spaces; $\Psi$-space
function spaces; $C_p(X,Y)$; Rothberger spaces; $\Psi$-space
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 $n\in\omega$.
References:
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