Zurück zu den Preprints des Jahres 1999


Sets with a large Borsuk number

by Weißbach, Bernulf.

Series: 1999-15, Preprints

52A20 Convex sets in $n$ dimensions (including convex hypersurfaces)

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.

Borsuk's problem