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

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

2006-11-08

arxiv.org/abs/math/0611239v1

Mathematics

General Topology

10 pages

Scientific paper

Given a Lie group $G$ we study the class $\M$ of proper metrizable $G$-spaces with metrizable orbit spaces, and show that any $G$-space $X \in \M$ 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 $\M$. As corollaries we see that any $G$-ANE for $\M$ has the $G$-homotopy type of some $G$-CW complex and that any $G$-ANR for $\M$ is a $G$-ANE for $\M$.

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