Abstract:A space $X$ is {discretely absolutely star-Lindel\"of} 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 $St(F,\Cal U)=X$, where $St(F,{\Cal U}) = \bigcup \{U\in {\Cal U} : U\cap F\not =\emptyset \}$. We show that every Hausdorff star-Lindel\"of space can be represented in a Hausdorff discretely absolutely star-Lindel\"of space as a closed subspace.
Keywords: normal, star-Lindel\"of, centered-Lindel\"of
AMS Subject Classification: 54D20, 54G20