The Stacks project

Definition 20.24.2. Let $X$ be a topological space. An open covering $X = \bigcup _{i \in I} U_ i$ is said to be locally finite if for every $x \in X$ there exists an open neighbourhood $W$ of $x$ such that $\{ i \in I \mid W \cap U_ i \not= \emptyset \} $ is finite.