A characterization of paracompactness of locally Lindelöf spaces

Abstract

A space $X$ is said to have property $B$ if every infinite open cover $\mathcal{U}$ of $X$ has an open refinement $mathcal{V}$ such that every point $x\in X$ has a neighborhood $W$ with $|\{V\in \mathcal{V}:W\cap V\neq\emptyset\}| \lt |mathcal{V}|$. It is proved that a locally Lindelof space is paracompact iff it has property $B$.