Some remarks on almost Lindel{ö}f spaces and weakly Lindel{ö}f spaces

Abstract

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