Preserving $Z$-sets by Dranishnikov's resolution

Details Preserving $Z$-sets by Dranishnikov's resolution Preserving $Z$-sets by Dranishnikov's resolution

2008-03-28

arxiv.org/abs/0803.4126v1

Topology Appl. 156:13 (2009), 2175-2188.

Mathematics

General Topology

Scientific paper

10.1016/j.topol.2009.04.003

We prove that Dranishnikov's $k$-dimensional resolution $d_k\colon \mu^k\to Q$ is a UV$^{n-1}$-divider of Chigogidze's $k$-dimensional resolution $c_k$. 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.

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