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Helly's Theorem


If F is a family of more than n bounded closed convex sets in Euclidean n-space 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

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References

Eckhoff, J. "Helly, Radon, and Carathéodory Type Theorems." Ch. 2.1 in Handbook of Convex Geometry (Ed. P. M. Gruber and J. M. Wills). Amsterdam, Netherlands: North-Holland, pp. 389-448, 1993.

Referenced on Wolfram|Alpha

Helly's Theorem

Cite this as:

Weisstein, Eric W. "Helly's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HellysTheorem.html

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