Antonyan, NatellaAntonyan, SergeyMartín Peinador, Elena2023-06-192023-06-192014-02-150166-864110.1016/j.topol.2013.10.003https://hdl.handle.net/20.500.14352/33448Ibero-American Conference on Topology and its Applications (CITA-2012)For a locally compact group G we consider the class G-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-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-M and V is a G-absolute extensor for the class G-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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0166864113003763#http://www.sciencedirect.com/restricted access515.1Locally compact groupProper G-spaceInvariant metricEquivariant embeddingBanach G-spaceGrupos (Matemáticas)Topología1210 Topología