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1997-25

Ein weiteres Gegenbeispiel zur Borsukschen Vermutung

by Grey, J., Weißbach, B..


Series: 1997-25, Preprints

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

Abstract:
1933 K. Borsuk raised the question whether every bounded set
M ae E d ; cardM 0 2, can be covered by at most d + 1 sets of smaller
diameter than M .
J. Kahn and G. Kalai showed in 1992 that this is not the case. The
smallest dimension d for which they obtained a counterexample is
d = 2016. A. Nilli constructs a counterexample for d = 946. We show
here that such a counterexample already exists for d = 903. The proof
follows a pattern from the construction of A. Nilli.

Keywords:
Borsuk's problem