Equivariant embeddings and compactifications of freeG-spaces

Abstract

For a compact Lie groupG, we characterize freeG-spaces that admit freeG-compactifications. For suchG-spaces, a universal compact freeG-space of given weight and given dimension is constructed. It is shown that ifGis finite, then-dimensional Menger freeG-compactumμ nis universal for all separable, metrizable freeG-spaces of dimension less than or equal ton. Some of these results are extended to the case ofG-spaces with a single orbit type.