Compacta with shapes of finite complexes: a direct approach to the Edwards-Geoghegan-Wall obstruction

TL;DR

This paper provides a straightforward, self-contained proof of a key stability theorem in shape theory, which characterizes compacta with the same shape as finite CW complexes.

Contribution

It offers a direct and simplified proof of the Edwards-Geoghegan-Wall obstruction theorem in shape theory.

Findings

Proof of the stability theorem is simplified and made self-contained.

Clarifies the relationship between compacta and finite CW complexes.

Enhances understanding of shape equivalence in topology.

Abstract

An important "stability" theorem in shape theory, due to D.A. Edwards and R. Geoghegan, characterizes those compacta having the same shape as a finite CW complex. In this note we present straightforward and self-contained proof of that theorem.