Embedding into discretely absolutely star-Lindelöf spaces

Song, Yan-Kui

Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 303-309.

Résumé

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.

Détail

Classification : 54C25, 54D20, 54G20
Keywords: normal; star-Lindelöf; centered-Lindelöf