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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 1, Pages 1-14
http://dx.doi.org/10.1155/S0161171203111155

Equivariant embeddings and compactifications of free G-spaces

1Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, D.F., México 04510, Mexico
2Departamento de Matemáticas-DIA, Instituto Tecnolo-gico de Monterrey, Calle del Puente 222, Ejidos de Huipulco, Tlalpan, D.F., México 14380, Mexico

Received 16 November 2001

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 μn 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.