Article ID Journal Published Year Pages File Type
4658617 Topology and its Applications 2014 14 Pages PDF
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
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