A proof of The Edwards-Walsh Resolution Theorem without Edwards-Walsh CW-complexes

Abstract

In the paper titled "Bockstein basis and resolution theorems in extension theory" (arXiv:0907.0491v2), we stated a theorem that we claimed to be a generalization of the Edwards-Walsh resolution theorem. The goal of this note is to show that the main theorem from (arXiv:0907.0491v2) is in fact equivalent to the Edwards-Walsh resolution theorem, and also that it can be proven without using Edwards-Walsh complexes. We conclude that the Edwards-Walsh resolution theorem can be proven without using Edwards-Walsh complexes.