Category:Helly's Theorem

This category contains pages concerning Helly's Theorem:

Let $A_1, A_2, \ldots, A_r \in \R^n$ be convex sets in real Euclidean $n$-space such that $r > n$.

Let $A_1, A_2, \ldots, A_r$ have the property that every collection of $n + 1$ of $A_1, A_2, \ldots, A_r$ have a point in common.

Then all of $A_1, A_2, \ldots, A_r$ have a point in common.