Bockstein basis and resolution theorems in extension theory

Abstract

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 $P_G=\{p\in \mathbb{P}:{\mathbb{Z}}_{(p)}\in$ 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 $0\le k<n$. 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) $\dim Z\le n$, and (c) $Z\tau K$.

arXiv comment23 pages