James H. Schmerl

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A theorem of Neumann-Lara and Urrutia [3] is generalized from the plane to arbitrary n-dimensional Euclidean space R n , solving Problem 2 of [3]. By an n-ball we mean a set of the form { Theorem 1. For each n ≥ 1 there is c n > 0 such that for any finite set X Õ R n there is A Õ X, |A| ≤ 1/ 2 (n+3) , having the following property: if B ⊇ A is an n-ball,(More)