Abstract
A subsetS of a real linear spaceE is said to bem-convex providedm≧2, there exist more thanm points inS, and for eachm distinct points ofS at least one of the ( m2 ) segments between thesem points is included inS. InE, letxy denote the segment between two pointsx andy. For any pointx inSυE, letS x ={y: xyυS}. The kernel of a setS is then defined as {xεS: S x=S}. It is shown that the kernel of a setS is always a subset of the intersection of all maximalm-convex subsets ofS. A sufficient condition is given for the intersection of all the maximalm-convex subsets of a setS to be the kernel ofS.
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Tattersall, J.J. On the intersection of maximalm-convex subsets. Israel J. Math. 16, 300–305 (1973). https://doi.org/10.1007/BF02756709
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DOI: https://doi.org/10.1007/BF02756709