Moebius and sub-Moebius structures

Abstract: We introduce a notion of a sub-Moebius structure and find necessary and sufficient conditions under which a sub-Moebius structure is a Moebius structure. We show that on the boundary at infinity of every Gromov hyperbolic space Y there is a canonical sub-Moebius structure which is invariant under isometries of Y such that the sub-Moebius topology on the boundary coincides with the standard one.