RETRACTION PROPERTIES OF AN ORBIT SPACE

Abstract

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.