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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
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