Approximation of k-dimensional maps

In this paper we prove the equivalence of the questions of Pasynkov [Dokl. Akad. Nauk SSSR 221 (1975) 543] and Uspenskij [Topology Appl. 85 (1998) 351]. We also get some partial results answering these questions in affirmative. As a corollary to these results we get an extention of the Hurewicz formula to the extensional dimension.