Local diameters of compact sets

Abstract

Abstract. Given, in a normed space, a compact set K and P ∈ K, let r(K, P) = max R∈K ||P − R||. For P 1 ∈ K we consider sequencesThe behaviour of such sequences for K contained in the Euclidean plane, and their limits were studied by Alarcon and Stolarsky in [1]. Here we try to sharpen some of their results and to extend them to a more general setting.Mathematics subject classification (2000): 26D15, 46B99, 46C99.