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Mat. Zametki, 1977, Volume 22, Issue 5, Pages 621–631 (Mi mz8086)  

This article is cited in 1 scientific paper (total in 1 paper)

Borsuk's problem

V. G. Boltyanskiia, V. P. Soltan

a V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: The Borsuk number of a bounded set $F$ is the smallest natural number $k$ such that $F$ can be represented as a union of $k$ sets, the diameter of each of which is less than $\operatorname{diam}F$. In this paper we solve the problem of finding the Borsuk number of any bounded set in an arbitrary two-dimensional normed space (the solution is given in terms of the enlargement of a set to a figure of constant width). We indicate spaces for which the solution of Borsuk's problem has the same form as in the Euclidean plane.

Full text: PDF file (975 kB)

English version:
Mathematical Notes, 1977, 22:5, 839–844

Bibliographic databases:

UDC: 513.82
Received: 15.09.1976

Citation: V. G. Boltyanskii, V. P. Soltan, “Borsuk's problem”, Mat. Zametki, 22:5 (1977), 621–631; Math. Notes, 22:5 (1977), 839–844

Citation in format AMSBIB
\Bibitem{BolSol77}
\by V.~G.~Boltyanskii, V.~P.~Soltan
\paper Borsuk's problem
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 5
\pages 621--631
\mathnet{http://mi.mathnet.ru/mz8086}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=482520}
\zmath{https://zbmath.org/?q=an:0368.52010}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 5
\pages 839--844
\crossref{https://doi.org/10.1007/BF01098346}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Raigorodskii, “Borsuk's problem and the chromatic numbers of some metric spaces”, Russian Math. Surveys, 56:1 (2001), 103–139  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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