Abstract

A space $X$ is almost Lindel{ö}f (weakly Lindel{ö}f) if for every open cover $\Cal U$ of $X$, there exists a countable subset $\Cal V$ of $\Cal U$ such that $\bigcup\{\overline{V}:V\in \Cal V\}=X$ (respectively, $\overline{\bigcup\Cal V}=X$). In this paper, we investigate the relationships among almost Lindel{ö}f spaces, weakly Lindel{ö}f spaces and Lindel{ö}f spaces, and also study topological properties of almost Lindel{ö}f spaces and weakly Lindel{ö}f spaces.

Keywords: Lindel{ö}f; almost Lindel{ö}f; weakly Lindel{ö}f.

MSC: 54D20, 54E18

Pages:  77$-$83     

Volume  62 ,  Issue  1 ,  2010