Locally solid convergence structures

2024/04/24 by Eugene Bilokopytov, Bilokopytov, E., J. Conradie +5 · 1 citation
Engineering · #54A20 #Advanced Materials and Mechanics #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 46A40. Secondary: 46A19 #Structural Analysis and Optimization #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2404.15641

openalex publication_date 2024/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of convergence structures, we develop a theory of locally solid convergences, which generalize locally solid topologies but also includes many important non-topological convergences on a vector lattice. We consider some natural modifications of such structures: unbounded, bounded, and Choquet. We also study some specific convergences in vector lattices from the perspective of locally solid convergence structures.

Cited by

• A counterexample regarding the relatively uniform completion of a principal ideal

Related

• Unbounded topologies and uo-convergence in locally solid vector lattices
• uτ-Convergence in locally solid vector lattices
• Composition of locally solid convergences
• Locally solid convergences and order continuity of positive operators
• Countability conditions in locally solid convergence spaces