Completeness in topological vector spaces and filters on \(\mathbb{N}\)

DOI10.36045/j.bbms.210512zbMath1497.46003arXiv2106.15192OpenAlexW4280530845MaRDI QIDQ2139114

Dmytro Seliutin, Vladimir Kadets

Publication date: 17 May 2022

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.15192

zbMATH Keywords

completenessidealfiltertopological vector space\(f\)-statistical convergence

Mathematics Subject Classification ID

Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) General theory of locally convex spaces (46A03) Ideal and statistical convergence (40A35)

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Cites Work

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• Weak statistical convergence and weak filter convergence for unbounded sequences
• A course in functional analysis and measure theory. Translated from the Russian by Andrei Iacob
• A characterization of Banach spaces with separable duals via weak statistical convergence
• Filter-dependent versions of the uniform boundedness principle
• \(f\)-statistical convergence, completeness and \(f\)-cluster points
• Density by moduli and statistical convergence
• Sur la convergence statistique

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