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 R<sup>n</sup> 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 Q<sup>n</sup> with the Euclidean metric and general metric l<sub>p</sub>.