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oai:docta.ucm.es:20.500.14352/334482023-08-27T05:16:23Zcom_20.500.14352_14col_20.500.14352_15

Antonyan, Natella Antonyan, Sergey Martín Peinador, Elena 2023-06-19T13:22:56Z 2023-06-19T13:22:56Z 2014-02-15 0166-8641 10.1016/j.topol.2013.10.003 https://hdl.handle.net/20.500.14352/33448 http://www.sciencedirect.com/science/article/pii/S0166864113003763# http://www.sciencedirect.com/ 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. eng restricted access Equivariant embeddings of metrizable proper G-spaces journal article