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.
Funding source: Ministry of Economy and Competitiveness of Spain
Award Identifier / Grant number: MTM2014-58984-P
Funding statement: The first author was supported by Research Grant number MTM2014-58984-P, awarded by the Ministry of Economy and Competitiveness of Spain.
References
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