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.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).