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Helly's Theorem

If $F$ is a family of more than $n$ bounded closed convex sets in Euclidean $n$-space $\Bbb{R}^n$, and if every $H_n$ (where $H_n$ is the Helly Number) members of $F$ have at least one point in common, then all the members of $F$ have at least one point in common.

See also Carathéodory's Fundamental Theorem, Helly Number




© 1996-9 Eric W. Weisstein
1999-05-25