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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



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
Published electronically: July 26, 2016
MathSciNet review: 3582948
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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

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Additional Information

P. V. Paramonov
Affiliation: Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Moscow 119991, Russia

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

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