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convex sets in euclidean space

Source: miklos schweitzer 2011 q6

August 29, 2021
real analysisEuclidean spaceConvex hullcombinatorial geometry

Problem Statement

Let C1,...,CdC_1, ..., C_d be compact and connected sets in RdR^d, and suppose that each convex hull of CiC_i contains the origin. Prove that for every i there is a ci∈Cic_i \in C_i for which the origin is contained in the convex hull of the points c1,...,cdc_1, ..., c_d.
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