On dentability and cones with a large dual

Abstract

In this paper, we provide some equivalences on dentability in normed spaces. Among others we prove: the origin is a denting point of a pointed cone $C$ if and only if it is a point of continuity for such a cone and $\overline{C^*-C^*}=X^*$; $x$ is a denting point of a convex set $A$ if and only if $x$ is a point of continuity and a weakly strongly extreme point of $A$. We also analize how our results help us to shed some light on several open problems in the literature.