The generalized Schoenflies theorem
نویسنده
چکیده
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.
منابع مشابه
On the Combinatorial Schoenflies Conjecture
Introduction. The combinatorial version of the Schoenflies conjecture in dimension n states: A combinatorial (n — l)-sphere on a combinatorial «-sphere decomposes the latter into two combinatorial ncells. The cases n = 1, 2 are obvious, the case n = 3 was solved by J. W. Alexander [l], see also W. Graeub [5], and E. Moise [8]. Nothing is known for n>3 (compare J. F. Hudson and E. C. Zeeman in [...
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