Discrete Set of Subsets is Locally Finite

Theorem

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

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

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

Proof

This follows immediately from the definitions of discrete set of subsets and locally finite set of subsets.

$\blacksquare$