Braß, Peter; Herburt, Irmina On point sets fixing a convex body from within. (English) Zbl 0887.52005 Beitr. Algebra Geom. 38, No. 1, 87-90 (1997). 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 PDFBibTeX XMLCite \textit{P. Braß} and \textit{I. Herburt}, Beitr. Algebra Geom. 38, No. 1, 87--90 (1997; Zbl 0887.52005) Full Text: EuDML EMIS