Definition:Finite Intersection Property

Definition
Let $\Bbb S$ be a non-empty set of sets.

Let $\Bbb S$ have the property that:
 * the intersection of any finite number of sets in $\Bbb S$ is not empty.

Then $\Bbb S$ satisfies the finite intersection property.

Also see

 * Do not confuse this with the Finite Intersection Axiom.