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dc.rights.licenseAtribución-NoComercial 4.0 Internacional
dc.contributor.authorFindley, D. F.
dc.date.accessioned2019-06-28T10:46:50Z
dc.date.available2019-06-28T10:46:50Z
dc.date.issued1974
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/42385
dc.description.abstractIn this note, we show that a strong form of the Bolzano-Weierstrass theorem in  a topological vector space E[ T] is equivalent, for example, to the assertion that there are enough differentiable paths,  x (t),  with non-trivial tangen t vectors, so that a function f defined  on E will be sequentially continuous for T if the composites f(x(t)) are all continuous. For a large class of locally convex spaces, this property is shown to be equivalent to the statement that the bounded sets of E[T] are finite dimensional. This leads to some very precise results for special cases.
dc.format.mimetypeapplication/pdf
dc.language.isospa
dc.publisherUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
dc.relationhttp://revistas.unal.edu.co/index.php/recolma/article/view/32009
dc.relation.ispartofUniversidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
dc.relation.ispartofRevista Colombiana de Matemáticas
dc.relation.ispartofseriesRevista Colombiana de Matemáticas; Vol. 8, núm. 4 (1974); 247-252 0034-7426
dc.rightsDerechos reservados - Universidad Nacional de Colombia
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/
dc.titleDifferentiable paths in topological vector spaces
dc.typeArtículo de revista
dc.type.driverinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dc.identifier.eprintshttp://bdigital.unal.edu.co/32482/
dc.relation.referencesFindley, D. F. (1974) Differentiable paths in topological vector spaces. Revista Colombiana de Matemáticas; Vol. 8, núm. 4 (1974); 247-252 0034-7426 .
dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.subject.proposalBolzano-Weierstrass theorem
dc.subject.proposaltopological vector spaces
dc.subject.proposalocally convex spaces
dc.subject.proposalbounded sets
dc.type.coarhttp://purl.org/coar/resource_type/c_6501
dc.type.coarversionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.contentText
dc.type.redcolhttp://purl.org/redcol/resource_type/ART
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2


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Atribución-NoComercial 4.0 InternacionalThis work is licensed under a Creative Commons Reconocimiento-NoComercial 4.0.This document has been deposited by the author (s) under the following certificate of deposit