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Inspired by a classical theorem of topological dimension theory, we prove that every geodesic metric space of asymptotic dimension n containing a bi-infinite geodesic can be coarsely separated by a subset S of asymptotic dimension equal to or smaller than n-1. \\ We define asymptotic Cantor manifolds, and we prove that every finitely generated group contains such a manifold. We also state some questions related to them.
Panagiotis Tselekidis (Sat,) studied this question.
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