Chains which are coset spaces of 𝑡𝑙-groups

Abstract

Let G G be a lattice-ordered group with a topology with which G G is a Hausdorff topological group and topological lattice. Let N N be a closed prime convex l l -subgroup of G G and let G / N G/N denote the topological chain of right cosets of N N . It is shown that if G G is locally compact, locally connected, or locally convex then G / N G/N is either discrete or has precisely the interval topology.