  Baker and Riley proved that a free group of rank 3 can be contained in a
hyperbolic group as a subgroup for which the Cannon-Thurston map is not
well-defined. By using their result, we show that the phenomenon occurs for not
only a free group of rank 3 but also every non-elementary hyperbolic group. In
fact it is shown that a similar phenomenon occurs for every non-elementary
relatively hyperbolic group.

Group Theory;Geometric Topology