Resumen de Convex sets without diametral pairs
Let X be an in¯nite dimensional normed linear space. It is not di±cult to see that arbitrarily near (in the Hausdor® metric) to the unit ball of X there exists a nonempty closed convex set whose diameter is not attained. We show that such sets are dense in the metric space of all nonempty bounded closed convex subsets of X if and only if either X is not a re°exive Banach space or X is a re°exive Banach space in which every weakly closed set contained in the unit sphere SX has empty relative interior in SX.
