# Definition:Point Finite

## Definition

Let $S$ be a set.

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

Then $\CC$ is point finite if and only if each element of $S$ is an element of finitely many sets in $\CC$:

$\forall s \in S: \card {\set {C \in \CC: s \in C} } < \infty$

## Also defined as

Some sources define point finite only for subsets of topological spaces.

Others define point finite only for covers.

In each case, however, the underlying meaning is identical.