We prove a general theorem about the orbit spaces of compact Lie group actions which are Hilbert cube manifolds. This result is further applied to prove that the Banach-Mazur compactum BM(2) is homeomorphic to the orbit ...

Extensorial properties of orbit spaces of locally compact proper group actions are investigated. (C) 1999 Elsevier Science B.V. All rights reserved.

Let G be a locally compact Hausdorff group. It is proved that: (1) on each Palais proper G-space X there exists a compatible family of Ginvariant pseudometrics

Let G be a locally compact Hausdorff group. We study orbit spaces of equivariant absolute neighborhood extensors (G-ANE's) in the category of all proper G-spaces that are metrizable by a G-invariant metric. We prove that ...

Let X be a Hausdorff topological group and G a locally compact subgroup of X. We show that the natural action of G on X is proper in the sense of R. Palais. This is applied to prove that there exists a closed set F subset ...

It is proved that: (1) every Lie group G can act properly (in sense of Palais) on each infinite-dimensional Hilbert space 12 (T) of a given weight tau such that (G, l(2) (tau)) becomes a universal G-space for all metrizable ...