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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 239, Pages 63–82
(Mi tm359)
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This article is cited in 8 scientific papers (total in 8 papers)
Borsuk's Conjecture, Ryshkov Obstruction, Interpolation, Chebyshev Approximation, Transversal Tverberg's Theorem, and Problems
S. A. Bogatyi M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
S. S. Ryshkov's solution of K. Borsuk's problem about $k$-regular embeddings is discussed. The results of Haar, Kolmogorov, and Rubinshtein are presented concerning the relation between $k$-regular mappings and interpolation, the number of zeros, and the low-dimensionality of the polyhedron of best Chebyshev approximations. The Tverberg transversal theorem is proved, and the place of the colored Tverberg theorem in the class of the problems discussed is highlighted. Many unsolved problems are formulated.
Received in May 2001
Citation:
S. A. Bogatyi, “Borsuk's Conjecture, Ryshkov Obstruction, Interpolation, Chebyshev Approximation, Transversal Tverberg's Theorem, and Problems”, Discrete geometry and geometry of numbers, Collected papers. Dedicated to the 70th birthday of professor Sergei Sergeevich Ryshkov, Trudy Mat. Inst. Steklova, 239, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 63–82; Proc. Steklov Inst. Math., 239 (2002), 55–73
Linking options:
https://www.mathnet.ru/eng/tm359 https://www.mathnet.ru/eng/tm/v239/p63
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Abstract page: | 584 | Full-text PDF : | 204 | References: | 47 |
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