Retraction properties of an orbit space

S. A. Antonyan

Sbornik. Mathematics, Tome 65 (1990) no. 2, pp. 305-321

Résumé

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.

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