Abstract
Let G be a locally compact Hausdorff group. We study orbit spaces and unions of equivariant absolute neighborhood extensors ( G- ANEs) in the category of all proper G-spaces that are metrizable by a G-invariant metric. We prove that if a proper G-space X is a G- ANE such that all the G-orbits in X are metrizable, then the G-orbit space X/ G is an ANE. Equivariant versions of Hanner's theorem and Kodama's theorem about unions of absolute neighborhood extensors are established. We also introduce the notion of a G-polyhedron and prove that if G is any compact group, then every G- ANR is arbitrary closely dominated by a G-polyhedron. Each G-polyhedron is a G- ANE.
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