Nonstandard analysis and differentiable manifolds - Foundations

Bibliographic Details
Main Author: Almeida, R
Publication Date: 2009
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/4151
Summary: 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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T03:33:20Zoai:ria.ua.pt:10773/4151Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:38:38.905033Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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