Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658617 | Topology and its Applications | 2014 | 14 Pages |
Abstract
For a locally compact group G we consider the class G-MG-M of all proper (in the sense of R. Palais) G-spaces that are metrizable by a G -invariant metric. We show that each X∈G-MX∈G-M admits a compatible G-invariant metric whose closed unit balls are small subsets of X. This is a key result to prove that X admits a closed equivariant embedding into an invariant convex subset V of a Banach G-space L such that L∖{0}∈G-ML∖{0}∈G-M and V is a G -absolute extensor for the class G-MG-M. On this way we establish two equivariant embedding results for proper G-spaces which may be considered as equivariant versions of the well-known Kuratowski–Wojdyslawski theorem and Arens–Eells theorem, respectively.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Natella Antonyan, Sergey Antonyan, Elena Martín-Peinador,