This article is cited in 1 paper

Borsuk's problem

V. G. Boltyanskii^a, 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.

UDC: 513.82

Received: 15.09.1976

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

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