Retraction properties of an orbit space

In this paper there is an investigation, for the case of a compact group $G$, of the orbit space $X/G$ of a given $G$-space $X$, from the point of view of the theory of retracts. A particular case of the main result asserts that if one of the spaces $X$ and $G$ has countable weight and $X$ is a $G$-A(N)R for metrizable spaces, then $X/G$ is an A(N)R for metrizable spaces.
New results about the equivariant embedding of metrizable $G$-spaces are also obtained.
Bibliography: 28 titles.