Memorandum on multiplicative bijections and order

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dc.authorid0000-0003-2687-6193en_US
dc.authorid0000-0003-0924-5189en_US
dc.authorid0000-0003-4600-1503
dc.contributor.authorCabello Sanchez, Felix
dc.contributor.authorCabello Sanchez, Javier
dc.contributor.authorErcan, Zafer
dc.contributor.authorÖnal, Süleyman
dc.date.accessioned2021-06-23T19:26:10Z
dc.date.available2021-06-23T19:26:10Z
dc.date.issued2009
dc.departmentBAİBÜ, Fen Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractLet C(X, I) denote the semigroup of continuous functions from the topological space X to I = [0, 1], equipped with the pointwise multiplication. The paper studies semigroup homomorphisms C(Y, I) -> C(X, I), with emphasis on isomorphisms. The crucial observation is that, in this setting, homomorphisms preserve order, so isomorphisms preserve order in both directions and they are automatically lattice isomorphisms. Applications to uniformly continuous and Lipschitz functions on metric spaces are given. Sample result: if Y and X are complete metric spaces of finite diameter without isolated points, every multiplicative bijection T : Lip(Y, I) -> Lip(X, I) has the form Tf = f circle tau, where tau : X -> Y is a Lipschitz homeomorphism.en_US
dc.identifier.doi10.1007/s00233-009-9152-2
dc.identifier.endpage209en_US
dc.identifier.issn0037-1912
dc.identifier.issn1432-2137
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-76349118537en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage193en_US
dc.identifier.urihttps://doi.org/10.1007/s00233-009-9152-2
dc.identifier.urihttps://hdl.handle.net/20.500.12491/6443
dc.identifier.volume79en_US
dc.identifier.wosWOS:000269015900013en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorErcan, Zafer
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofSemigroup Forumen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectSemigroups of Continuous Functionsen_US
dc.subjectHomomorphismen_US
dc.subjectRepresentationen_US
dc.titleMemorandum on multiplicative bijections and orderen_US
dc.typeArticleen_US

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