  We prove a generalization of the Edwards-Walsh Resolution Theorem:
  Theorem: Let G be an abelian group for which $P_G$ equals the set of all
primes $\mathbb{P}$, where $P_G=\{p \in \mathbb{P}: \Z_{(p)}\in$ Bockstein
Basis $ \sigma(G)\}$. Let n in N and let K be a connected CW-complex with
$\pi_n(K)\cong G$, $\pi_k(K)\cong 0$ for $0\leq k< n$. Then for every compact
metrizable space X with $X\tau K$ (i.e., with $K$ an absolute extensor for
$X$), there exists a compact metrizable space Z and a surjective map $\pi: Z
\to X$ such that (a) $\pi$ is cell-like, (b) $\dim Z \leq n$, and (c) $Z\tau
K$.
