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Equivariant embeddings of metrizable proper G-spaces

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Antonyan, Natella and Antonyan, Sergey and Martín Peinador, Elena (2014) Equivariant embeddings of metrizable proper G-spaces. Topology and its Applications, 163 . pp. 11-24. ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/article/pii/S0166864113003763#


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Abstract

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.


Item Type:Article
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Ibero-American Conference on Topology and its Applications (CITA-2012)

Uncontrolled Keywords:Locally compact group; Proper G-space; Invariant metric; Equivariant embedding; Banach G-space
Subjects:Sciences > Mathematics > Group Theory
Sciences > Mathematics > Topology
ID Code:24216
Deposited On:15 Jan 2014 14:04
Last Modified:12 Dec 2018 15:12

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