Definition 5.28.4. Let $X$ be a topological space. Let $I$ be a set and for $i \in I$ let $E_ i \subset X$ be a subset. We say the collection $\{ E_ i\} _{i \in I}$ is locally finite if for all $x \in X$ there exists an open neighbourhood $U$ of $x$ such that $\{ i \in I | E_ i \cap U \not= \emptyset \}$ is finite.

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