Equivariant embedding of metrizable G-spaces in linear G-spaces

الأصل · EN

Given a Lie group G we study the class of proper metrizable G-spaces with metrizable orbit spaces, and show that any G-space X ∈ admits a closed G-embedding into a convex G-subset C of some locally convex linear G-space, such that X has some G-neighborhood in C which belongs to the class. As corollaries we see that any G-ANE for has the G-homotopy type of some G-CW complex and that any G-ANR for is a G-ANE for.