Equivariant embeddings of metrizable proper G-spaces

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dc.contributor.authorAntonyan, Natella
dc.contributor.authorAntonyan, Sergey
dc.contributor.authorMartín Peinador, Elena
dc.date.accessioned2023-06-19T13:22:56Z
dc.date.available2023-06-19T13:22:56Z
dc.date.issued2014-02-15
dc.descriptionIbero-American Conference on Topology and its Applications (CITA-2012)
dc.description.abstractFor 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.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipCONACYT (Mexico).
dc.description.sponsorshipCONACYT (Mexico).
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/24216
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dc.identifier.doi10.1016/j.topol.2013.10.003
dc.identifier.issn0166-8641
dc.identifier.officialurlhttp://www.sciencedirect.com/science/article/pii/S0166864113003763#
dc.identifier.relatedurlhttp://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/33448
dc.journal.titleTopology and its Applications
dc.language.isoeng
dc.page.final24
dc.page.initial11
dc.publisherElsevier Science
dc.relation.projectID165195
dc.relation.projectID165246
dc.rights.accessRightsrestricted access
dc.subject.cdu515.1
dc.subject.keywordLocally compact group
dc.subject.keywordProper G-space
dc.subject.keywordInvariant metric
dc.subject.keywordEquivariant embedding
dc.subject.keywordBanach G-space
dc.subject.ucmGrupos (Matemáticas)
dc.subject.ucmTopología
dc.subject.unesco1210 Topología
dc.titleEquivariant embeddings of metrizable proper G-spaces
dc.typejournal article
dc.volume.number163
dspace.entity.typePublication
relation.isAuthorOfPublication0074400c-5caa-43fa-9c45-61c4b6f02093
relation.isAuthorOfPublication.latestForDiscovery0074400c-5caa-43fa-9c45-61c4b6f02093
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