The Canonical Schoenflies Theorem


M. Brown has shown that if f:Sn~1Xl'—»5", where /' = [ — 1, 1], is an embedding, then the closure of either complementary domain of/(5"_1X0) is homeomorphic to Bn; in fact there is an embedding g : Bn—*Sn satisfying g | 5"-1 =/| 5n_1 X 0. This paper shows that the choice of embedding g can be made to be "canonical," i.e. if /' is an embedding near / in the compact-open sense, then the embedding g' corresponding to/' is near g.

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Cite this paper

@inproceedings{Gauld2010TheCS, title={The Canonical Schoenflies Theorem}, author={David Gauld}, year={2010} }