An elementary example of Sard's Theorem sharpness

In this note we define a C1 function F : [0, M] 2 → [0, 2] that satisfies that its set of critical values has positive measure. This function provides an example, easier than those that usually appear in the literature, of how the order of differentiability required in Sard’s Theorem cannot be impro...

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Detalhes bibliográficos
Autor: Ferrera Cuesta, Juan
Formato: artículo
Fecha de publicación:2022
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/71710
Acesso em linha:https://hdl.handle.net/20.500.14352/71710
Access Level:acceso abierto
Palavra-chave:517
Morse-Sard Theorem
Cantor set
Matemáticas (Matemáticas)
Análisis matemático
12 Matemáticas
1202 Análisis y Análisis Funcional
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oai_identifier_str oai:docta.ucm.es:20.500.14352/71710
network_acronym_str ES
network_name_str España
repository_id_str
spelling An elementary example of Sard's Theorem sharpnessFerrera Cuesta, Juan517Morse-Sard TheoremCantor setMatemáticas (Matemáticas)Análisis matemático12 Matemáticas1202 Análisis y Análisis FuncionalIn this note we define a C1 function F : [0, M] 2 → [0, 2] that satisfies that its set of critical values has positive measure. This function provides an example, easier than those that usually appear in the literature, of how the order of differentiability required in Sard’s Theorem cannot be improved.Universidad Complutense de Madrid20222022-02-1720222022-02-17journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/71710reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/717102026-06-02T12:44:21Z
dc.title.none.fl_str_mv An elementary example of Sard's Theorem sharpness
title An elementary example of Sard's Theorem sharpness
spellingShingle An elementary example of Sard's Theorem sharpness
Ferrera Cuesta, Juan
517
Morse-Sard Theorem
Cantor set
Matemáticas (Matemáticas)
Análisis matemático
12 Matemáticas
1202 Análisis y Análisis Funcional
title_short An elementary example of Sard's Theorem sharpness
title_full An elementary example of Sard's Theorem sharpness
title_fullStr An elementary example of Sard's Theorem sharpness
title_full_unstemmed An elementary example of Sard's Theorem sharpness
title_sort An elementary example of Sard's Theorem sharpness
dc.creator.none.fl_str_mv Ferrera Cuesta, Juan
author Ferrera Cuesta, Juan
author_facet Ferrera Cuesta, Juan
author_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517
Morse-Sard Theorem
Cantor set
Matemáticas (Matemáticas)
Análisis matemático
12 Matemáticas
1202 Análisis y Análisis Funcional
topic 517
Morse-Sard Theorem
Cantor set
Matemáticas (Matemáticas)
Análisis matemático
12 Matemáticas
1202 Análisis y Análisis Funcional
description In this note we define a C1 function F : [0, M] 2 → [0, 2] that satisfies that its set of critical values has positive measure. This function provides an example, easier than those that usually appear in the literature, of how the order of differentiability required in Sard’s Theorem cannot be improved.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-02-17
2022
2022-02-17
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/71710
url https://hdl.handle.net/20.500.14352/71710
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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