A theorem on intersection with a $k$-dimensional barycenter
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V. A. Malyshev
Translated by: the author - St. Petersburg Math. J. 17 (2006), 635-640
- DOI: https://doi.org/10.1090/S1061-0022-06-00923-X
- Published electronically: May 3, 2006
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Abstract:
For a multidimensional analog of the barycenter (which is a certain union of intervals), a multidimensional analog of the following statement is proved: if a continuous mapping maps each face of a simplex into itself, then the image of the mapping meets the barycenter.References
- V. A. Rokhlin and D. B. Fuks, Nachal′nyĭ kurs topologii: geometricheskie glavy, Izdat. “Nauka”, Moscow, 1977 (Russian). MR 0645388
Bibliographic Information
- V. A. Malyshev
- Affiliation: Rybinsk State Aviation Technology Academy, Rybinsk, Russia
- Email: wmal@ryb.adm.yar.ru
- Received by editor(s): September 10, 2004
- Published electronically: May 3, 2006
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 17 (2006), 635-640
- MSC (2000): Primary 26C10, 57Q15, 41A50
- DOI: https://doi.org/10.1090/S1061-0022-06-00923-X
- MathSciNet review: 2173938