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Tr. Mat. Inst. Steklova, 2002, Volume 239, Pages 63–82 (Mi tm359)  

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 239, 55–73

Bibliographic databases:

UDC: 515.127.15
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, Tr. Mat. Inst. Steklova, 239, Nauka, MAIK Nauka/Inteperiodika, M., 2002, 63–82; Proc. Steklov Inst. Math., 239 (2002), 55–73

Citation in format AMSBIB
\Bibitem{Bog02}
\by S.~A.~Bogatyi
\paper Borsuk's Conjecture, Ryshkov Obstruction, Interpolation, Chebyshev Approximation, Transversal Tverberg's Theorem, and Problems
\inbook Discrete geometry and geometry of numbers
\bookinfo Collected papers. Dedicated to the 70th birthday of professor Sergei Sergeevich Ryshkov
\serial Tr. Mat. Inst. Steklova
\yr 2002
\vol 239
\pages 63--82
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm359}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1975135}
\zmath{https://zbmath.org/?q=an:1069.57500}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 239
\pages 55--73


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    This publication is cited in the following articles:
    1. A. Yu. Volovikov, “The genus of $G$-spaces and topological lower bounds for chromatic numbers of hypergraphs”, J. Math. Sci., 144:5 (2007), 4387–4397  mathnet  crossref  mathscinet  zmath  elib  elib
    2. A. Yu. Volovikov, “Coincidence points of maps of $\mathbb Z_p^n$-spaces”, Izv. Math., 69:5 (2005), 913–962  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. S. A. Bogatyi, V. M. Valov, “Roberts-type embeddings and conversion of transversal Tverberg's theorem”, Sb. Math., 196:11 (2005), 1585–1603  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Bogatyi S.A., “Finite–to–one maps”, Topology and Its Applications, 155:17–18 (2008), 1876–1887  crossref  mathscinet  zmath  isi  scopus
    5. Arocha J.L., Bracho J., Montejano L., Alfonsin J.L.R., “Transversals to the convex hulls of all k-sets of discrete subsets of R-n”, J Combin Theory Ser A, 118:1 (2011), 197–207  crossref  mathscinet  zmath  isi  elib  scopus
    6. S. I. Bogataya, S. A. Bogatyi, E. A. Kudryavtseva, “An inverse theorem on ‘economic’ maps”, Sb. Math., 203:4 (2012), 554–568  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. K. I. Oblakov, T. A. Oblakova, “Embeddings of graphs into Euclidean space under which the number of points that belong to a hyperplane is minimal”, Sb. Math., 203:10 (2012), 1518–1533  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. S. A. Bogatyi, “Generic planes conjecture”, Moscow University Mathematics Bulletin, 67:5-6 (2012), 200–205  mathnet  crossref
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