Bockstein basis and resolution theorems in extension theory

英文摘要：

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 $ σ(G)\}$. Let n in N and let K be a connected CW-complex with $π_n(K)\cong G$, $π_k(K)\cong 0$ for $0\leq k< n$. Then for every compact metrizable space X with $XτK$ (i.e., with $K$ an absolute extensor for $X$), there exists a compact metrizable space Z and a surjective map $π: Z \to X$ such that (a) $π$ is cell-like, (b) $\dim Z \leq n$, and (c) $ZτK$.