Definition:Point Finite

Definition
Let $S$ be a set.

Let $\mathcal C$ be a set of subsets of $S$.

Then $\mathcal C$ is point finite each element of $S$ is an element of finitely many sets in $\mathcal C$:
 * $\forall s \in S: \left\vert{ \left\{{ C \in \mathcal C: s \in C }\right\} }\right\vert < \infty$

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.

Also see

 * Definition:Metacompact Space
 * Definition:Locally Finite Cover