Definition 3.12.1 (Locally Finite).label Let $X$ be a topological space and $\cali{U}\suf \cali{P}(X)$, then $\cali{U}$ is locally finite if for each $x\in X$, there exists $V\in\cali{N}(x)$ such that $\curl{U\in\cali{U}:V\cap U\neq\emp}$ is finite. Let $U\suf X$ and define $\cali{U}\define \curl{\curl{x}:x\in U}$ then we say $U$ is locally finite if $\cali{U}$ is locally finite.