A counterexample regarding the relatively uniform completion of a principal ideal

2025/06/11 by Youssef Azouzi, Azouzi, Youssef · 1 citation
Mathematics · #06F20 #46A40 #Advanced Banach Space Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Functional Analysis (math.FA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2506.09798

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a counterexample related to relative uniform convergence, showing that, in general, the relatve uniform completion of the principal ideal of a vector lattice E generated by an element x is stricly contained in the ideal generated by x in the relatively uniform completion of E.

Citations

• About the relatively uniform completion of a principal ideal
• Locally solid convergence structures
• Net convergence structures with applications to vector lattices
• Bibasic sequences in Banach lattices

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• About the relatively uniform completion of a principal ideal

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