Universal acyclic resolutions for arbitrary coefficient groups

Abstract

We prove that for every compactum $X$ and every integer $n\ge 2$ there are a compactum $Z$ of $\dim \le n+1$ and a surjective $U{V}^{n-1}$-map $r: Z \lo X$ such that for every abelian group $G$ and every integer $k\ge 2$ such that ${\dim }_{G}X\le k\le n$ we have ${\dim }_{G}Z\le k$ and $r$ is $G$-acyclic.