Now showing items 1-2 of 2

    • IconA lower bound for the equilateral number of normed spaces  [Article]

      Swanepoel, Konrad J.; Villa Caro, Rafael (American Mathematical Society, 2008)
      We show that if the Banach-Mazur distance between an n-dimensional normed space X and ℓ n∞ is at most 3/2, then there exist n + 1 equidistant points in X. By a well-known result of Alon and Milman, this implies that an ...
    • IconMaximal equilateral sets  [Article]

      Swanepoel, Konrad J.; Villa Caro, Rafael (Springer, 2013-09)
      A subset of a normed space X is called equilateral if the distance between any two points is the same. Let m(X) be the smallest possible size of an equilateral subset of X maximal with respect to inclusion. We first observe ...