Helly's selection theorem

Helly's selection theorem is a result in combinatorial geometry and convex analysis, named after the mathematician Eduard Helly. The theorem asserts conditions under which a family of convex sets possesses a point in common, based on the intersections of smaller subfamilies of those sets. The precise statement of Helly's selection theorem typically involves a finite collection of convex sets in \(\mathbb{R}^d\).