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On point sets fixing a convex body from within. (English) Zbl 0887.52005
For a convex body $$K \subset \mathbb{R}^d$$ a finite subset $$S$$ is called fixing $$K$$ from within if any translation $$t\neq 0$$ moves at least on point of $$S$$ outside $$K$$.
In answering a question of V. Soltan, the authors show that any finite $$S$$ fixing a $$d$$-dimensional body $$K$$ from within contains a subset of a most $$2d$$ points with the same property.
Reviewer: W.Weil (Karlsruhe)
MSC:
 52A35 Helly-type theorems and geometric transversal theory 52A20 Convex sets in $$n$$ dimensions (including convex hypersurfaces) 52C99 Discrete geometry
Keywords:
convex body; fixing set; minimal number
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