Countability conditions in locally solid convergence spaces

2025/01/20 by Eugene Bilokopytov, Bilokopytov, Eugene, Viktor Bohdanskyi +3
Mathematics · #46A40. Secondary: 54D55 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 46A19

paper · pdf · doi:10.48550/arxiv.2501.11517

openalex publication_date 2025/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively unform-, order-, and σ-order convergence, respectively, is (strongly) first countable. The implications for the validity of sequential arguments in the contexts of these convergences are pointed out.

Related

• Locally solid convergence structures
• Composition of locally solid convergences
• Unbounded topologies and uo-convergence in locally solid vector lattices
• Unbounded Order Convergence and Universal Completions
• uτ-Convergence in locally solid vector lattices