Inner structure in real vector spaces
-
Francisco Javier García-Pacheco
and
Enrique Naranjo-Guerra
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
[1] N. Bourbaki, Topological Vector Spaces. Chapters 1–5, Elements Math. (Berlin), Springer, Berlin, 1987. 10.1007/978-3-642-61715-7Search in Google Scholar
[2] F. J. García-Pacheco, Non-continuous linear functionals on topological vector spaces, Banach J. Math. Anal. 2 (2008), no. 1, 11–15. 10.15352/bjma/1240336267Search in Google Scholar
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- Oscillation of first-order differential equations with several non-monotone retarded arguments
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Articles in the same Issue
- Frontmatter
- Stability analysis of delay integro-differential equations of HIV-1 infection model
- Oscillation of first-order differential equations with several non-monotone retarded arguments
- Idempotent matrices with invertible transpose
- Some algebraic aspects of the gluing of differential spaces
- Inner structure in real vector spaces
- Averaged semi-discrete scheme of sum-approximation for one nonlinear multi-dimensional integro-differential parabolic equation
- Differential and integral equations for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials
- On adjoint resolutions and dimensions of modules
- Approximation by modified Jain–Baskakov operators
- Carleson measure and Volterra type operators on weighted BMOA spaces
- The effect of perturbations of frames and fusion frames on their redundancies
- Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces
- Trigonometric identities inspired by the atomic form factor
- W(Lp,Lq) boundedness of localization operators associated with the Stockwell transform
- Voronovskaja’s theorem for functions with exponential growth
- A quantitative Balian–Low theorem for higher dimensions
- Lp(·)–Lq(·) boundedness of some integral operators obtained by extrapolation techniques
- Statistical convergence of multiple sequences on a product time scale
