The space of circular orderings and semiconjugacy

Work of Linnell shows that the space left-orderings a group is either finite or uncountable, and in case finite, isomorphism type known—it what known as Tararin group. By defining semiconjugacy circular orderings general setting (that is, for arbitrary groups may not act on S1), we can view subspace any single class orderings. Taking this perspective, generalize result Linnell, to show every when has prescribed structure. We also investigate orderings, addressing question Baik Samperton.