Embedding into discretely absolutely star-Lindelöf spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 303-309
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A space $X$ is {\it discretely absolutely star-Lindelöf\/} if for every open cover $\Cal U$ of $X$ and every dense subset $D$ of $X$, there exists a countable subset $F$ of $D$ such that $F$ is discrete closed in $X$ and $\operatorname{St}(F,\Cal U)=X$, where $\operatorname{St}(F,{\Cal U}) = \bigcup \{U\in{\Cal U} : U\cap F\neq \emptyset \}$. We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed subspace.
A space $X$ is {\it discretely absolutely star-Lindelöf\/} if for every open cover $\Cal U$ of $X$ and every dense subset $D$ of $X$, there exists a countable subset $F$ of $D$ such that $F$ is discrete closed in $X$ and $\operatorname{St}(F,\Cal U)=X$, where $\operatorname{St}(F,{\Cal U}) = \bigcup \{U\in{\Cal U} : U\cap F\neq \emptyset \}$. We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed subspace.
@article{CMUC_2007_48_2_a11,
author = {Song, Yan-Kui},
title = {Embedding into discretely absolutely {star-Lindel\"of} spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {303--309},
year = {2007},
volume = {48},
number = {2},
mrnumber = {2338098},
zbl = {1199.54147},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2007_48_2_a11/}
}
Song, Yan-Kui. Embedding into discretely absolutely star-Lindelöf spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 303-309. http://geodesic.mathdoc.fr/item/CMUC_2007_48_2_a11/