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 $\mathcal{U}$ of $X$, there exists a countable subset $\mathcal{V}$of $\mathcal{U}$ such that $\bigcup \{\bar{V}:Vın\mathcal{V}\}\mathcal{=}\mathcal{X}$(respectively, $\overline{\bigcup \mathcal{V}}=X$). 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.