Preserving $Z$-sets by Dranishnikov's resolution

We prove that Dranishnikov’s $k$-dimensional resolution $d_k\colon \mu^k\to Q$isaUV$^{n-1}$-dividerofChigogidz{e}^{\mathrm{\prime }}s$k$-dimensionalresolution$c_k$. This fact implies that $d_k^{-1}$ preserves $Z$-sets. A further development of the concept of UV${}^{n-1}$-dividers permits us to find sufficient conditions for $d_k^{-1}(A)$ to be homeomorphic to the N"{o}beling space ${\nu }^k$ or the universal pseudoboundary ${\sigma }^k$. We also obtain some other applications.