On geometry of cones and some applications

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.