Bockstein basis and resolution theorems in extension theory

We prove a generalization of the Edwards–Walsh Resolution Theorem: Theorem be an abelian group with P G = P , where P G = { p ∈ P : Z ( p ) ∈ Bockstein basis σ ( G ) } . Let n ∈ N and let K be a connected CW-complex with π n ( K ) ≅ G , π k ( K ) ≅ 0 for 0 ⩽ 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 → X such that(a) ell-like, ⩽ n , and