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The generalized Schoenflies theorem

The generalized Schoenflies theorem asserts that if φ ∶ Sn−1 → S is a topological embedding and A is the closure of a component of Sn∖φ(Sn−1), then A ≅ D as long as A is a manifold. This was originally proved by Barry Mazur and Morton Brown using rather different techniques. We give both of these proofs.