The order convergence structure

Abstract

In this paper, we study order convergence and the order convergence structure in the context of σ -distributive lattices. Particular emphasis is placed on spaces with additional algebraic structure: we show that on a Riesz algebra with σ -order continuous multiplication, the order convergence structure is an algebra convergence structure, and construct the convergence vector space completion of an Archimedean Riesz space with respect to the order convergence structure.