On some analogs of Borsuk's problem in the space Q<sup>n</sup>
In 1933, K. Borsuk conjectured that each set of diameter 1 in Rn can be partitioned into n + 1 parts of smaller diameter. This conjecture was disproved in 1993. We consider various generalizations of Borsuk's problem to the cases of sets which lie in the space Qn with the Euclidean metric and general metric lp.