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Tbilisi Mathematical Journal

Editor-in-Chief: Inassaridze, Hvedri

2 Issues per year


Mathematical Citation Quotient (MCQ) 2016: 0.14

Open Access
Online
ISSN
1512-0139
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A note on closedness of algebraic sum of sets

Hubert Przybycień
Published Online: 2016-11-08 | DOI: https://doi.org/10.1515/tmj-2016-0020

Abstract

In this note we generalize the fact that in topological vector spaces the algebraic sum of closed set A and compact set B is closed. We also prove some conditions that are equivalent to reflexivity of Banach spaces.

Keywords: Closed convex sets

References

  • [1] A. Alexiewicz, Functional Analysis (1969) (in Polish)Google Scholar

  • [2] J. Dieudonne, Sur la sparation des ensembles convexes, Math. Ann. 163 (1966)Google Scholar

  • [3] Robert C. James, Reexivity and the sup of linear functionals, Israel J. Math 13 (1972), 3-4Google Scholar

  • [4] W. Rudin, Functional Analysis, McGraw-Hill Book Company, New York, 1973Google Scholar

About the article

Received: 2016-02-14

Accepted: 2016-09-16

Published Online: 2016-11-08

Published in Print: 2016-12-01


Citation Information: Tbilisi Mathematical Journal, Volume 9, Issue 2, Pages 71–74, ISSN (Online) 1512-0139, DOI: https://doi.org/10.1515/tmj-2016-0020.

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© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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