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Ultimately increasing functions

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Ultimately increasing functions

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dc.contributor.author Beer, Gerald es_ES
dc.contributor.author Rodríguez López, Jesús es_ES
dc.date.accessioned 2016-02-05T12:37:36Z
dc.date.available 2016-02-05T12:37:36Z
dc.date.issued 2010
dc.identifier.issn 0147-1937
dc.identifier.uri http://hdl.handle.net/10251/60658
dc.description.abstract A function gg between directed sets ⟨Σ,⪰′⟩⟨Σ,⪰′⟩ and ⟨Λ,⪰⟩⟨Λ,⪰⟩ is called \emph{ultimately increasing} if for each σ1∈Σσ1∈Σ there exists σ2⪰′σ1σ2⪰′σ1 such that σ⪰′σ2⇒g(σ)⪰g(σ1)σ⪰′σ2⇒g(σ)⪰g(σ1). A subnet of a net aa defined on ⟨Λ,⪰⟩⟨Λ,⪰⟩ \cite {Ke} is nothing but a composition of the form a∘ga∘g where gg is ultimately increasing and g(Σ)g(Σ) is a cofinal subset of ΛΛ. While even for linearly ordered sets, an increasing net defined on a cofinal subset of the domain need not have an increasing extension, in complete generality, it must have an ultimately increasing extension, and conversely when the domain is linearly ordered. Applications are given in the context of functions with values in a linearly ordered set equipped with the order topology - in particular, the extended real numbers. For example, we show that a real sequence ⟨an⟩⟨an⟩ converges to the supremum of its set of terms if and only if ⟨an⟩⟨an⟩ is the supremum of the ultimately increasing sequences that it majorizes. es_ES
dc.language Inglés es_ES
dc.publisher Michigan State University Press es_ES
dc.relation.ispartof Real analysis Exchange es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Ultimately increasing function es_ES
dc.subject Monotone convergence theorem es_ES
dc.subject In- creasing function es_ES
dc.subject Subnet es_ES
dc.subject Directed set es_ES
dc.subject Chain es_ES
dc.subject Order topology es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Ultimately increasing functions es_ES
dc.type Artículo es_ES
dc.rights.accessRights Cerrado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Beer, G.; Rodríguez López, J. (2010). Ultimately increasing functions. Real analysis Exchange. 36(1):195-212. http://hdl.handle.net/10251/60658 es_ES
dc.description.accrualMethod Senia es_ES
dc.relation.publisherversion https://projecteuclid.org/all/euclid.rae es_ES
dc.description.upvformatpinicio 195 es_ES
dc.description.upvformatpfin 212 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 36 es_ES
dc.description.issue 1 es_ES
dc.relation.senia 208817 es_ES


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