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may 2022 Completeness in topological vector spaces and filters on $\mathbb N$
Vladimir Kadets, Dmytro Seliutin
Bull. Belg. Math. Soc. Simon Stevin 28(4): 531-545 (may 2022). DOI: 10.36045/j.bbms.210512

Abstract

We study completeness of a topological vector space with respect to different filters on $\mathbb N$. In the metrizable case all these kinds of completeness are the same, but in non-metrizable case the situation changes. For example, a space may be complete with respect to one ultrafilter on $\mathbb N$, but incomplete with respect to another. Our study was motivated by [Aizpuru, Listán-García and Rambla-Barreno; Quaest. Math., 2014] and [Listán-García; Bull. Belg. Math. Soc. Simon Stevin, 2016] where for normed spaces the equivalence of the ordinary completeness and completeness with respect to $f$-statistical convergence was established.

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Vladimir Kadets. Dmytro Seliutin. "Completeness in topological vector spaces and filters on $\mathbb N$." Bull. Belg. Math. Soc. Simon Stevin 28 (4) 531 - 545, may 2022. https://doi.org/10.36045/j.bbms.210512

Information

Published: may 2022
First available in Project Euclid: 11 May 2022

Digital Object Identifier: 10.36045/j.bbms.210512

Subjects:
Primary: 40A35 , 54A20

Keywords: $f$-statistical convergence , completeness , filter‎ , ideal , topological vector space

Rights: Copyright © 2022 The Belgian Mathematical Society

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Vol.28 • No. 4 • may 2022
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