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St. Petersburg Mathematical Journal

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



A theorem on intersection with a $ k$-dimensional barycenter

Author: V. A. Malyshev
Translated by: the author
Original publication: Algebra i Analiz, tom 17 (2005), nomer 4.
Journal: St. Petersburg Math. J. 17 (2006), 635-640
MSC (2000): Primary 26C10, 57Q15, 41A50
Published electronically: May 3, 2006
MathSciNet review: 2173938
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Abstract | References | Similar Articles | Additional Information

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

  • 1. V. A. Rokhlin and D. B. Fuks, \cyr Nachal′nyĭ kurs topologii: geometricheskie glavy., Izdat. “Nauka”, Moscow, 1977 (Russian). MR 0645388
    D. B. Fuks and V. A. Rokhlin, Beginner’s course in topology, Universitext, Springer-Verlag, Berlin, 1984. Geometric chapters; Translated from the Russian by A. Iacob; Springer Series in Soviet Mathematics. MR 759162

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Additional Information

V. A. Malyshev
Affiliation: Rybinsk State Aviation Technology Academy, Rybinsk, Russia

Keywords: Barycenter
Received by editor(s): September 10, 2004
Published electronically: May 3, 2006
Article copyright: © Copyright 2006 American Mathematical Society