Statement
Suppose that
is a finite collection of convex subsets of, where . If the intersection of every of these sets is nonempty, then the whole collection has a nonempty intersection; that is,
For infinite collections one has to assume compactness: If is a collection of compact convex subsets of and every subcollection of cardinality at most has nonempty intersection, then the whole collection has nonempty intersection.
Read more about this topic: Helly's Theorem
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