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Keywords:
normal; star-Lindelöf; centered-Lindelöf
normal; star-Lindelöf; centered-Lindelöf
Summary:
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.
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