An n-dimensional version of Steinhaus' chessboard theorem |
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| Authors: | Przemys?aw Tkacz |
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| Affiliation: | College of Science, Cardinal Stefan Wyszyński, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa, Poland |
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| Abstract: | The main result of this paper is an n-dimensional version of the Steinhaus' chessboard theorem. Our theorem implies the Poincaré theorem as well as its parametric extension. But it is known that the Poincaré theorem is equivalent to the Brouwer Fixed-Point theorem. |
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| Keywords: | primary, 54H25, 54-04 secondary, 55M20, 54F55, 52B15 |
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