The Completion of an Abelian l-Group

Abstract

A directed partially ordered abelian group (G, ≦ ) is a tight Riesz group if for a1, a2, b1, b2 ∈ G with ai < bj, i, j = 1,2, there is an x ∈ G with ai < x < bj, i, j = 1, 2. The open interval topology on G is the topology having as a base the set of all open intervals (a, b) = {x ∈ G|a < x < b}. For any x ∈ G, a neighborhood base at x is the set of all open intervals (x — a, x + a) = x + ( — a, a) for a > 0.