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Borsuk asked in 1933 if every set of diameter 1 in $R^d$ can be covered by$d+1$ sets of smaller diameter. In 1993, a negative solution, based on atheorem by Frankl and Wilson, was given by Kahn and Kalai. In this paper I willpresent questions related to Borsuk's problem.

Some old and new problems in combinatorial geometry I: Around Borsuk's problem