Adjunction spaces and unions of G-ANE's

Abstract

Let G be a locally compact Hausdorff group. We study adjunction spaces and unions of equivariant absolute neighborhood extensors (G-ANE's) in the category of all proper G-spaces that axe metrizable by G-invariant metrics. We establish equivariant versions of the Borsuk-Whitehead-Hanner Theorem and of the Kodama Theorem. As an application, we prove that every proper G-CW complex is a G-ANE provided G is a Lie group.