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A Helly-type theorem for the dimension of the kernel of a starshaped set

This study will investigate the dimension of the kernel of a starshaped set, and the following result will be obtained: Let S be a compact set in some linear topological space L. For 1 0 and some n-dimeinsional flat Fn in L, every f(n, k) points of S see via S a common k-dimensional neighborhood in Fn having radius e. The number f(n, k) is defined inductively as follows: