Nonstandard analysis and differentiable manifolds - Foundations

Detalhes bibliográficos
Autor(a) principal: Almeida, R
Data de Publicação: 2009
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/4151
Resumo: We approach the study of di erentiable manifolds modeled on Banach spaces by means of Nonstandard Analysis. We stay inside the category of classical manifolds and using nonstandard analysis techniques, we present some new nonstandard characterizations for the tangent bundle, di erentiable function, di erential of a function, directional derivatives, etc. We establish some relations between our de nitions and the classical ones.
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spelling Nonstandard analysis and differentiable manifolds - FoundationsNonstandard analysisdifferentiable manifoldstangent bundleinfinitesimal transformationWe approach the study of di erentiable manifolds modeled on Banach spaces by means of Nonstandard Analysis. We stay inside the category of classical manifolds and using nonstandard analysis techniques, we present some new nonstandard characterizations for the tangent bundle, di erentiable function, di erential of a function, directional derivatives, etc. We establish some relations between our de nitions and the classical ones.Balkan Society of Geometers2011-10-13T11:04:48Z2009-01-01T00:00:00Z2009info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/4151eng1454-511XAlmeida, Rinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:04:29Zoai:ria.ua.pt:10773/4151Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:42:12.577658Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Nonstandard analysis and differentiable manifolds - Foundations
title Nonstandard analysis and differentiable manifolds - Foundations
spellingShingle Nonstandard analysis and differentiable manifolds - Foundations
Almeida, R
Nonstandard analysis
differentiable manifolds
tangent bundle
infinitesimal transformation
title_short Nonstandard analysis and differentiable manifolds - Foundations
title_full Nonstandard analysis and differentiable manifolds - Foundations
title_fullStr Nonstandard analysis and differentiable manifolds - Foundations
title_full_unstemmed Nonstandard analysis and differentiable manifolds - Foundations
title_sort Nonstandard analysis and differentiable manifolds - Foundations
author Almeida, R
author_facet Almeida, R
author_role author
dc.contributor.author.fl_str_mv Almeida, R
dc.subject.por.fl_str_mv Nonstandard analysis
differentiable manifolds
tangent bundle
infinitesimal transformation
topic Nonstandard analysis
differentiable manifolds
tangent bundle
infinitesimal transformation
description We approach the study of di erentiable manifolds modeled on Banach spaces by means of Nonstandard Analysis. We stay inside the category of classical manifolds and using nonstandard analysis techniques, we present some new nonstandard characterizations for the tangent bundle, di erentiable function, di erential of a function, directional derivatives, etc. We establish some relations between our de nitions and the classical ones.
publishDate 2009
dc.date.none.fl_str_mv 2009-01-01T00:00:00Z
2009
2011-10-13T11:04:48Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/4151
url http://hdl.handle.net/10773/4151
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1454-511X
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Balkan Society of Geometers
publisher.none.fl_str_mv Balkan Society of Geometers
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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