Analysis of D-disjointness in partially ordered vector spaces reveals new properties for discrete elements, suggesting connections to vector lattices.
The notions of disjointness and discrete elements play a prominent role in the classical theory of vector lattices. There are at least three different generalizations of the notion of disjointness to a larger class of partially ordered vector spaces. In recent years, one of these generalizations has been widely studied in the context of pre-Riesz spaces. The notion of D-disjointness is the most general of the three disjointness concepts. In this paper we study D-disjointness and the related concept of a D-discrete element. We establish some basic properties of D-discrete elements in Archimedean partially ordered spaces, and we investigate their relationship to discrete elements in the theory of pre-Riesz spaces.
No takes yet. Share an insight, caveat, or question.
Jani Jokela (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: