\begin{definition}[Definition:Point Finite]
Let $S$ be a set.
Let $\CC$ be a set of subsets of $S$.
Then $\CC$ is '''point finite''' {{iff}} each element of $S$ is an element of finitely many sets in $\CC$:
:$\forall s \in S: \card {\set {C \in \CC: s \in C} } < \infty$
\end{definition}