The Rothberger property on
Commentationes Mathematicae Universitatis Carolinae (2016)
- Volume: 57, Issue: 1, page 83-88
- ISSN: 0010-2628
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topBernal-Santos, Daniel. "The Rothberger property on $C_p(\Psi (\mathcal {A}),2)$." Commentationes Mathematicae Universitatis Carolinae 57.1 (2016): 83-88. <http://eudml.org/doc/276758>.
@article{Bernal2016,
abstract = {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 $.},
author = {Bernal-Santos, Daniel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {function spaces; $C_p(X,Y)$; Rothberger spaces; $\Psi $-space},
language = {eng},
number = {1},
pages = {83-88},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The Rothberger property on $C_p(\Psi (\mathcal \{A\}),2)$},
url = {http://eudml.org/doc/276758},
volume = {57},
year = {2016},
}
TY - JOUR
AU - Bernal-Santos, Daniel
TI - The Rothberger property on $C_p(\Psi (\mathcal {A}),2)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 1
SP - 83
EP - 88
AB - 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 $.
LA - eng
KW - function spaces; $C_p(X,Y)$; Rothberger spaces; $\Psi $-space
UR - http://eudml.org/doc/276758
ER -
References
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