Preserving Z-sets by Dranishnikovʹs resolution

We prove that Dranishnikovʹs k-dimensional resolution d k : μ k → Q is a UVn − 1-divider of Chigogidzeʹs k-dimensional resolution c k . This fact implies that d k − 1 preserves Z-sets. A further development of the concept of UVn − 1-dividers permits us to find sufficient conditions for d k − 1 ( A ) to be homeomorphic to the Nöbeling space ν k or the universal pseudoboundary σ k . We also obtain some other applications.