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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2017: 0.23

Online
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1572-9176
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Inner structure in real vector spaces

Francisco Javier García-PachecoORCID iD: http://orcid.org/0000-0001-6208-6071 / Enrique Naranjo-GuerraORCID iD: http://orcid.org/0000-0001-8817-8820
Published Online: 2018-07-20 | DOI: https://doi.org/10.1515/gmj-2018-0048

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.

Keywords: Internal point; convex; balanced; absorbing

MSC 2010: 54C05; 46A03; 46A55

References

  • [1]

    N. Bourbaki, Topological Vector Spaces. Chapters 1–5, Elements Math. (Berlin), Springer, Berlin, 1987. 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. CrossrefWeb of ScienceGoogle Scholar

About the article

Received: 2016-05-04

Revised: 2016-10-25

Accepted: 2016-11-04

Published Online: 2018-07-20


Funding Source: Ministry of Economy and Competitiveness of Spain

Award identifier / Grant number: MTM2014-58984-P

The first author was supported by Research Grant number MTM2014-58984-P, awarded by the Ministry of Economy and Competitiveness of Spain.


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0048.

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