Differentiable paths in topological vector spaces

In 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 sequentiall...

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Autores:: Findley, D. F.

Tipo de recurso:: Article of journal

Fecha de publicación:: 1974

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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spelling	Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Findley, D. F.d46fa2b8-63ff-429b-b0e0-2322946c7c5d3002019-06-28T10:46:50Z2019-06-28T10:46:50Z1974https://repositorio.unal.edu.co/handle/unal/42385http://bdigital.unal.edu.co/32482/In 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.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/32009Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 8, núm. 4 (1974); 247-252 0034-7426Findley, D. F. (1974) Differentiable paths in topological vector spaces. Revista Colombiana de Matemáticas; Vol. 8, núm. 4 (1974); 247-252 0034-7426 .Differentiable paths in topological vector spacesArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTBolzano-Weierstrass theoremtopological vector spacesocally convex spacesbounded setsORIGINAL32009-117324-1-PB.pdfapplication/pdf1796003https://repositorio.unal.edu.co/bitstream/unal/42385/1/32009-117324-1-PB.pdfe7e1dbe6858ae2bd8daeb55894fbdef5MD51THUMBNAIL32009-117324-1-PB.pdf.jpg32009-117324-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg7281https://repositorio.unal.edu.co/bitstream/unal/42385/2/32009-117324-1-PB.pdf.jpgf16be7b669e92479d7720c0bf38a9247MD52unal/42385oai:repositorio.unal.edu.co:unal/423852024-02-04 23:07:06.538Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv	Differentiable paths in topological vector spaces
title	Differentiable paths in topological vector spaces
spellingShingle	Differentiable paths in topological vector spaces Bolzano-Weierstrass theorem topological vector spaces ocally convex spaces bounded sets
title_short	Differentiable paths in topological vector spaces
title_full	Differentiable paths in topological vector spaces
title_fullStr	Differentiable paths in topological vector spaces
title_full_unstemmed	Differentiable paths in topological vector spaces
title_sort	Differentiable paths in topological vector spaces
dc.creator.fl_str_mv	Findley, D. F.
dc.contributor.author.spa.fl_str_mv	Findley, D. F.
dc.subject.proposal.spa.fl_str_mv	Bolzano-Weierstrass theorem topological vector spaces ocally convex spaces bounded sets
topic	Bolzano-Weierstrass theorem topological vector spaces ocally convex spaces bounded sets
description	In 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.
publishDate	1974
dc.date.issued.spa.fl_str_mv	1974
dc.date.accessioned.spa.fl_str_mv	2019-06-28T10:46:50Z
dc.date.available.spa.fl_str_mv	2019-06-28T10:46:50Z
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dc.relation.spa.fl_str_mv	http://revistas.unal.edu.co/index.php/recolma/article/view/32009
dc.relation.ispartof.spa.fl_str_mv	Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv	Revista Colombiana de Matemáticas; Vol. 8, núm. 4 (1974); 247-252 0034-7426
dc.relation.references.spa.fl_str_mv	Findley, D. F. (1974) Differentiable paths in topological vector spaces. Revista Colombiana de Matemáticas; Vol. 8, núm. 4 (1974); 247-252 0034-7426 .
dc.rights.spa.fl_str_mv	Derechos reservados - Universidad Nacional de Colombia
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dc.publisher.spa.fl_str_mv	Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
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Differentiable paths in topological vector spaces

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