  In this paper we first extend from normed spaces to locally convex spaces
some characterizations of denting points in convex sets. On the other hand, we
also prove that in an infrabarreled locally convex space a point in a convex
set is denting if and only if it is a point of continuity and an extreme point
of the closure of such a convex set under the strong topology in the second
dual. The version for normed spaces of the former equivalence is new and
contains, as particular cases, some known and remarkable results. We also
extend from normed spaces to locally convex spaces some known characterizations
of the weak property (\(\pi\)) of cones. Besides, we provide some new results
regarding the angle property of cones and related. We also state that the class
of cones in normed spaces having a pointed completion is the largest one for
which the vertex is a denting point if and only if it is a point of continuity.
Finally we analyse and answer several problems in the literature concerning
geometric properties of cones which are related with density problems into
vector optimization.
