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.

在本文中，我们首先从赋范空间扩展到局部凸空间，凸集上凹点的一些特征。另一方面，我们也证明了，在且仅当它是连续点和在强拓扑下这种凸集封闭的一个极端点时，在一个桶形局部凸空间中的一个凸集才是凹点。第二个双重。前等价范数空间的版本是新的，并且在特定情况下还包含一些已知且引人注目的结果。我们还将从赋范空间扩展到局部凸空间的一些弱属性的已知特征（\（\ pi \））的视锥细胞。此外，我们提供了一些有关圆锥体及其相关角度特性的新结果。我们还指出，当且仅当连续点是顶点时，范数空间中具有尖头完成度的圆锥体类别是顶点最大的圆锥体。最后，我们分析并回答了有关锥的几何特性的文献中的几个问题，这些问题与矢量优化中的密度问题有关。