Equivariant embeddings and compactifications of free G-spaces

Abstract

For a compact Lie group G, we characterize free G-spaces that admit free G-compactifications. For such G-spaces, a universal compact free G-space of given weight and given dimension is constructed. It is shown that if G is finite, the n-dimensional Menger free G-compactum μ n is universal for all separable, metrizable free G-spaces of dimension less than or equal to n. Some of these results are extended to the case of G-spaces with a single orbit type.