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 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.
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