Definition:Closed Locally Finite Set of Subsets

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $\FF$ be a set of subsets of $S$.

Then $\UU$ is closed locally finite :
 * $(1) \quad \forall F \in \FF: S \setminus F \in \tau$, that is, for all $F \in \FF: F$ is closed in $T$
 * $(2) \quad \FF$ is locally finite