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On starshapedness of the union of closed sets in $${\mathbb{R}}^ n$$. (English) Zbl 0635.52006
It is shown that Helly’s Theorem is equivalent to the following: Let F be a finite family of closed sets in $${\mathbb{R}}^ n;$$ if any $$n+1$$ members of F has a starshaped union, then ker($$\cup F)\neq \emptyset$$. The kernel of a set consists of the points that can ‘see’ all points of the set. Using a theorem of Katchalski, a lower bound for the dimension of ker($$\cup F)$$ is determined.
Reviewer: G.Sierksma

##### MSC:
 52A35 Helly-type theorems and geometric transversal theory 52A30 Variants of convex sets (star-shaped, ($$m, n$$)-convex, etc.)
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