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Helly's theorem

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Helly's theorem

[′hel·ēz ‚thir·əm]
(mathematics)
The theorem that there is a point that belongs to each member of a collection of bounded closed convex sets in an n-dimensional Euclidean space if the collection has at least n + 1 members and any n + 1 members of the collection have a common point.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive
It describes the linear or vector space concepts of addition and scalar multiplication, linear subspaces, linear functionals, and hyperplanes, as well as different distances in n-space and the geometric properties of subsets, subspaces, and hyperplanes; topology in the context of metrics derived from a norm on the n-dimensional space; the concept of convexity and the basic properties of convex sets; and Helly's theorem and applications involving transversals of families of pairwise disjoint compact convex subsets of the plane.
Geometry of Convex Sets
The Centerpoint Theorem, which is a simple consequence of Helly's Theorem [6], states that for any point set S of size n there exists a point whose halfspace depth is at least [n/(d + 1)].
Centerpoint theorems for wedges
By Helly's Theorem, there exists a weak-star limit [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] along some subsequence [LAMBDA] [subset] N.
On extremal problems related to inverse balayage
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