Topological concepts in partially ordered vector spaces

TL;DR

This paper explores various types of order convergence and topologies in partially ordered vector spaces, analyzing their relationships and differences to deepen understanding of their mathematical structure.

Contribution

It systematically investigates and relates multiple notions of order convergence and topologies introduced by different researchers in the context of partially ordered vector spaces.

Findings

Clarifies relationships between different order topologies

Provides a comparative analysis of convergence concepts

Enhances understanding of the structure of ordered vector spaces

Abstract

In the context of partially ordered vector spaces one encounters different sorts of order convergence and order topologies. This article will investigate these notions and their relations. In particular we study and relate the order topology presented by Floyd, Vulikh and Dobbertin, the order bound topology studied by Namioka and the concept of order convergence given in the works of Abramovich, Sirotkin,Wolk and Vulikh.