nLab
locally finite cover

Definition

A cover (open cover) $\{U_{\alpha }\}$ of a topological space $X$ is locally finite if for all $x\in X$, there is an neighbourhood $N\ni x$ such that $N\cap U_{\alpha }\ne \varnothing$ for only a finite number of $\alpha$.

Open covers defined by partitions of unity are locally finite. (CHECK!)

Related concepts

• cover, open cover,

• paracompact topological space