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Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 2008, Volume 150, Book 1, Pages 124–129 (Mi uzku648)  

Combinatorial Lemma for Lebesgue–Brouwer Partition of Cube on Euclidean Space

R. R. Shagidullin

Kazan State University

Abstract: The purpose of this article is to present a new combinatorial lemma that can be used in fixed point theorem, for example, to prove Brouwer theorem. Partition of a three-dimensional cube used by Lebesgue and Brouwer in dimension theory is taken into consideration. Explanation is given for generalization of the lemma on Euclidean $n$-space, $n>3$.

Keywords: combinatorial lemma, fixed point theorem.

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Bibliographic databases:
UDC: 519.6
Received: 26.10.2007

Citation: R. R. Shagidullin, “Combinatorial Lemma for Lebesgue–Brouwer Partition of Cube on Euclidean Space”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 150, no. 1, Kazan University, Kazan, 2008, 124–129

Citation in format AMSBIB
\Bibitem{Sha08}
\by R.~R.~Shagidullin
\paper Combinatorial Lemma for Lebesgue--Brouwer Partition of Cube on Euclidean Space
\serial Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki
\yr 2008
\vol 150
\issue 1
\pages 124--129
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku648}
\zmath{https://zbmath.org/?q=an:05657162}


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