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 if and only if:

$(1) \quad \forall F \in \FF: S \setminus F \in \tau$, that is, for all $F \in \FF: F$ is closed in $T$

$(2) \quad \FF$ is locally finite

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