Abstract

A space $X$ is $C$-Lindel{ö}f (weakly $C$-Lindel{ö}f) if for every closed subset $F$ of $X$ and every open cover $\cal U$ of $F$ by open subsets of $X$, there exists a countable subfamily $\cal V$ of $\cal U$ such that $F\subseteq \cup\{\overline V:V \in\cal V\}$ (respectively, $F\subseteq \overline{\cup \cal V}$). In this paper, we investigate the relationships among $C$-Lindel{ö}f spaces, weakly $C$-Lindel{ö}f spaces and Lindel{ö}f spaces, and also study various properties of weakly $C$-Lindel{ö}f spaces and $C$-Lindel{ö}f spaces.

Keywords: Lindelöf space, $C$-Lindelöf space, weakly $C$-Lindelöf space.

MSC: 54D15, 54D20

Pages:  173$-$180     

Volume  60 ,  Issue  3 ,  2008