In this paper we prove that all model spaces of the most important infinite dimensional spaces are special cases of a single construction. We study the properties of this construction and prove classification and characterization theorems. Our results unify and complete existing characterizing results of H.Torunczyk, K.Sakai, E.Shchepin, and A.Chigogidze. In 2008 the journal Topology was placed on the Science Citation Index list on the 32th place among 214 journals.
COBISS.SI-ID: 15526233
We discuss spaces modelled on the Hilbert space, Nöbeling, and Menger spaces, and k-dimensional Dranishnikov resolution. Dranišnikov constructed in 1986 a particular resolution from the k-dimensional Menger compactum onto the Hilbert cube and proved several nice properties of this map. There was an open question whether the preimage of a Z-set (a subspace from which the space can be removed by an arbitrarily small continuous move) is again a Z-set. In a negative answr was given to this question, but it turned out to be a mistake. We succeeded in giving a positive answer.
COBISS.SI-ID: 15194201