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A characterization of paracompactness of locally Lindelöf spaces
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 …