finite intersection property of a family of sets

finite intersection property of a family of sets

[¦fī‚nīt‚in·tər′sek·shən ‚präp·ərd·ē əv ə ′fam·lē əv ′sets]
(mathematics)
If the intersection of any finite number of them is nonempty, then the intersection of all the members of the family is nonempty.