Abstract Internal points were introduced in the literature of topological vector spaces to characterize the finest locally convex vector topology. In this manuscript we generalize the concept of internal point in real vector spaces by introducing a type of points, called inner points, that allows us to provide an intrinsic characterization of linear manifolds, which was not possible by using internal points. We also characterize infinite dimensional real vector spaces by means of the inner points of convex sets. Finally, we prove that in convex sets containing internal points, the set of inner points coincides with the one of internal points.

中文翻译：

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实向量空间中的内部结构

摘要 在拓扑向量空间的文献中引入了内部点来表征最好的局部凸向量拓扑。在这篇手稿中，我们通过引入一种称为内点的点来概括实向量空间中内点的概念，这使我们能够提供线性流形的内在表征，这是使用内点无法实现的。我们还通过凸集的内点来刻画无限维实向量空间。最后，我们证明在包含内部点的凸集中，内部点的集合与内部点之一重合。