Abstract
Abstract.Baker and Riley gave an inclusion of a free group of rank 3 in a hyperbolic group for which the Cannon–Thurston map is not well-defined. By using their result, we show that every non-elementary hyperbolic group can be included in some hyperbolic group in such a way that the Cannon–Thurston map is not well-defined. In fact we generalize their result to every non-elementary relatively hyperbolic group.
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