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

TL;DR

This paper demonstrates that the Edwards-Walsh resolution theorem can be proven without Edwards-Walsh complexes, showing the equivalence of a related theorem and simplifying the proof approach.

Contribution

It proves the Edwards-Walsh resolution theorem without Edwards-Walsh complexes, establishing the equivalence of a previous generalization and simplifying the proof method.

Findings

The main theorem is equivalent to the Edwards-Walsh resolution theorem.

The proof can be achieved without Edwards-Walsh complexes.

The previous generalization does not extend beyond the original theorem.

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.