Locally Finite Set of Subsets is Sigma-Locally Finite Set of Subsets

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

Let $\AA$ be a locally finite set of subsets.

Then:
 * $\AA$ is a $\sigma$-locally finite set of subsets

Proof
For each $n \in \N$, let
 * $\AA_n = \AA$.

Then:
 * $\AA = \ds \bigcup_{n \in \N} \AA_n$

The result follows.