The Osgood–Schoenflies theorem revisited

L. Siebenmann

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 4, pp. 645-672

Résumé

The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned.

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