Rational acyclic resolutions

Abstract

Let $X$ be a compactum such that ${dim}_{\mathbb{Q}}X\le n$, $n\ge 2$. We prove that there is a $\mathbb{Q}$–acyclic resolution $r:Z\to X$ from a compactum $Z$ of $dim\le n$. This allows us to give a complete description of all the cases when for a compactum $X$ and an abelian group $G$ such that ${dim}_{G}X\le n$, $n\ge 2$ there is a $G$–acyclic resolution $r:Z\to X$ from a compactum $Z$ of $dim\le n$.