On geometry of cones and some applications

Abstract

In this work we prove that in any normed space, the origin is a denting point of a pointed cone if and only if it is a point of continuity for the cone and the closure of the cone in the bidual space with respect to the weak* topology is pointed. Other related results and consequences are also stated. For example, a criterion to know whether a cone has a bounded base, an unbounded base, or does not have any base; and a result on the existence of super efficient points in weakly compact sets.