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Tverberg's proof of the Jordan closed curve theorem


Authors: P. V. Paramonov and K. Yu. Fedorovsky
Translated by: A. Yu. Luzgarev
Original publication: Algebra i Analiz, tom 27 (2015), nomer 5.
Journal: St. Petersburg Math. J. 27 (2016), 851-860
MSC (2010): Primary 57N05; Secondary 30C99
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.


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Additional 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

DOI: https://doi.org/10.1090/spmj/1421
Keywords: Jordan curve, Jordan's theorem
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.
Article copyright: © Copyright 2016 American Mathematical Society