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 $\overline{C^{\ast }-C^{\ast }}=X^{\ast }$; $x$ 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.

Cited by in corpus (2)

• Sublinear Scalarizations for Proper and Approximate Proper Efficient Points in Nonconvex Vector Optimization
• Denting Points of Convex Sets and Weak Property ($\pi$) of Cones in Locally Convex Spaces