Sigma-Discrete Set of Subsets is Sigma-Locally Finite

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Theorem

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

Let $\FF$ be a $\sigma$-discrete set of subsets of $S$.

Then $\FF$ is a $\sigma$-locally finite set of subsets of $S$.

Proof

This follows immediately from:

Definition:Discrete Set of Subsets

Definition:Locally Finite Set of Subsets

Discrete Set of Subsets is Locally Finite

$\blacksquare$