Topologies arising from metrics valued in abelian ℓ-groups

摘要: This paper considers metrics valued in abelian l-groups and their induced topologies. In addition to a metric into an l-group, one needs filter the positive cone determine which balls are neighborhoods of center. As key special case, we discuss topology on lattice ordered group from dG consisting weak units G; case \({\mathbb R^{n}}\) , this is Euclidean topology. We also show that there many Nachbin convex topologies l-group not by any l-group.