Abstract
In this note we prove the following Helly type result. Theorem. LetXbe a collection of subsets of annelement setSwith the property that anykmembers ofXhave an element in common. IfXhas at least$(k + 2)2^{n - k - 1} + 1$members, then all members ofXhave an element in common. The same statement fails for bounds of one less for$n\geqq k + 1$.
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