Tverberg’s proof of the Jordan closed curve theorem
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P. V. Paramonov and K. Yu. Fedorovsky
Translated by: A. Yu. Luzgarev - St. Petersburg Math. J. 27 (2016), 851-860
- DOI: https://doi.org/10.1090/spmj/1421
- Published electronically: July 26, 2016
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Abstract:
A proof of the classical theorem on a simple closed curve (Jordan’s theorem) is discussed; this proof is given by a Norwegian mathematician H. Tverberg and is little known to specialists. The proof has a metric nature and makes it possible to obtain an important metric refinement of Jordan’s theorem, which is interesting on its own.References
- C. Jordan, Cours d’analyse de l’Ecole polytechnique. vol. 3, Gauthier-Villars, Paris, 1887, pp. 587–594.
- Helge Tverberg, A proof of the Jordan curve theorem, Bull. London Math. Soc. 12 (1980), no. 1, 34–38. MR 565480, DOI 10.1112/blms/12.1.34
Bibliographic Information
- P. V. Paramonov
- Affiliation: Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Moscow 119991, Russia
- Email: petr.paramonov@list.ru
- K. Yu. Fedorovsky
- Affiliation: Bauman Moscow State Technical University, 2-nd Baumanskaya str. 5, 105005 Moscow, Russia; Saint Petersburg State University, Department of Mathematics and Mechanics, Universitetsky pr. 28, St. Petersburg 198504, Russia
- Email: kfedorovs@yandex.ru
- Received by editor(s): April 14, 2015
- Published electronically: July 26, 2016
- Additional Notes: The second author was supported by Dmitri Zimin’s ‘Dynasty’ Foundation and by a Simons–IUM fellowship.
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 851-860
- MSC (2010): Primary 57N05; Secondary 30C99
- DOI: https://doi.org/10.1090/spmj/1421
- MathSciNet review: 3582948