o:1034936 Quasi-Isometries Need Not Induce Homeomorphisms of Contracting Boundaries with the Gromov Product Topology en We consider a ‘contracting boundary’ of a proper geodesic metric space consisting of equivalence classes of geodesic rays that behave like geodesics in a hyperbolic space. We topologize this set via the Gromov product, in analogy to the topology of the boundary of a hyperbolic space. We show that when the space is not hyperbolic, quasi-isometries do not necessarily give homeomorphisms of this boundary. Continuity can fail even when the spaces are required to be CAT(0). We show this by constructing an explicit example. 2019-10-21T09:08:36.125Z 44 yes 46 Christopher Cashen University of Vienna 0000-0002-6340-469X application/pdf 384771 http://phaidra.univie.ac.at/o:1034936 no yes 16 70 1552253 Analysis and Geometry in Metric Spaces 4:278-281 4 278 281 De Gruyter 2016