Convergence via filter in locally solid Riesz spaces

2018/03/07 by Abdullah Aydın, Aydın, Abdullah
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1803.02534

5 pages

arxiv created 2018/03/07 · openalex publication_date 2018/03/07 · arxiv updated 2018/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (E,τ) be a locally solid vector lattice. A filter F on the set E is said to be converge to a vector e∈ E if, each zero neighborhood set U containing e, U belongs to F. We study on the concept of this convergence and give some basic properties of it.

Related

• The statistically unbounded τ-convergence on locally solid Riesz spaces
• uτ-Convergence in locally solid vector lattices
• Locally solid convergence structures
• Lattice uniformities inducing unbounded convergence
• Unbounded topologies and uo-convergence in locally solid vector lattices