A note on adjunction spaces and G-ANE's

TL;DR

This paper offers a new proof of the equivariant Borsuk-Whitehead-Hanner Theorem for proper G-spaces with G-invariant metrics, enhancing understanding of G-ANE spaces.

Contribution

It presents an alternative proof of a fundamental theorem in equivariant topology specifically for proper G-spaces with G-invariant metrics.

Findings

Provides a different proof of the equivariant Borsuk-Whitehead-Hanner Theorem.

Clarifies the structure of proper G-spaces that are metrizable by G-invariant metrics.

Contributes to the theory of G-ANE spaces and their properties.

Abstract

We provide a different proof of the equivariant version of the Borsuk-Whitehead-Hanner Theorem in the category of proper G-spaces which are metrizable by a G-invariant metric.