99-15
Sets with a large Borsuk number
Preprint series: 99-15, Preprints
Abstract: We construct sets in Euclidean spaces of dimension d= $(4m-2 \over 2)$, where m is a power of a prime, with the property that they can only be coverd with a large number of sets having smaller diameter. Thereby we generalize a result of A. M. Raigorodskii and, in addition, we prove that there exists a counterexample to the so called \'Borsuk-conjecture\' already in dimension $(34 \over 2) - 1 = 560$.
Keywords: Borsuk\'s problem
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