The Space of Relative Orders and a Generalization of Morris Indicability Theorem

We introduce the space of relative orders on a group and show that it is compact whenever the group is finitely generated. We use this to show that if G is a finitely generated group acting on the line by order preserving homeomorphisms and some stabilizer of a point is a proper and co-amenable subgroup, then G surjects onto Z. This is a generalization of a theorem of Morris. © 2021 World Scientific Publishing Company.