97-25
Ein weiteres Gegenbeispiel zur Borsukschen Vermutung
by Grey, J.; Weißbach, B. (Magdeburg)
Preprint series: 97-25, Preprints
Abstract: In 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