Conjuntos semialgébricos e o teorema da finitude topológica

Detalhes bibliográficos
Ano de defesa: 2022
Autor(a) principal: Tanure, André Dantas
Orientador(a): Fernandes, Alexandre César Gurgel
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Geometria algébrica real
Conjuntos semialgébricos
Real algebraic geometry
Semi-algebraic sets
Link de acesso: http://www.repositorio.ufc.br/handle/riufc/68082
Resumo: We present the definition of a semialgebraic subset of Rn, that is a subset defined by a boolean condition of polynomial conditions. We show the first structure theorem for semialgebraic sets, The Cylindrical Decomposition Theorem and explore some of its consequences, in particular the Tarski-Seidenberg Theorem. Then we prove the second structure theorem, The Stratifi cation Theorem. After that, we explore some of its consequences, in particular the concept of dimension, and a version of Sard’s Theorem for semialgebraic mappings. We then present the concepts of Cell Decomposition and Triangulation of a set, and we prove that every compact semialgebraic set admits both a cell decomposition and a triangulation. We then enunciate the Local Triviality Theorem and present two applications: The Theorem on the Finiteness of Topological Types of semialgebraic sets, and the Local Conical Structure Lemma.
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spelling Tanure, André DantasFernandes, Alexandre César Gurgel2022-09-08T14:55:17Z2022-09-08T14:55:17Z2022-08-11TANURE, André Dantas. Conjuntos semialgébricos e o teorema da finitude topológica. 2022. 71 f. Dissertação (Mestrado Acadêmico em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2022.http://www.repositorio.ufc.br/handle/riufc/68082We present the definition of a semialgebraic subset of Rn, that is a subset defined by a boolean condition of polynomial conditions. We show the first structure theorem for semialgebraic sets, The Cylindrical Decomposition Theorem and explore some of its consequences, in particular the Tarski-Seidenberg Theorem. Then we prove the second structure theorem, The Stratifi cation Theorem. After that, we explore some of its consequences, in particular the concept of dimension, and a version of Sard’s Theorem for semialgebraic mappings. We then present the concepts of Cell Decomposition and Triangulation of a set, and we prove that every compact semialgebraic set admits both a cell decomposition and a triangulation. We then enunciate the Local Triviality Theorem and present two applications: The Theorem on the Finiteness of Topological Types of semialgebraic sets, and the Local Conical Structure Lemma.Apresentamos a definição de conjunto semialgébrico em Rn, que é um conjunto definido por uma condição booleana de condições polinomiais. Demonstramos o primeiro teorema de estrutura para conjuntos semialgébricos, o Teorema da Decomposição Cilíndrica, e exploramos suas consequências, em particular o Teorema de Tarski-Seidenberg. Depois, apresentamos o segundo Teorema de estrutura para conjuntos semialgébricos, o Teorema da Estratificação. Em seguida, exploramos suas consequências, em particular a noção de dimensão, e uma versão do Teorema de Sard para funções semialgébricas. Apresentamos as noções de Decomposição Celular e de Triangulação, e provamos que todo conjunto semialgébrico compacto é triangulável. Por fim, enunciamos o Teorema da Trivialidade Local e apresentamos duas consequências, o Teorema da Finitude de Tipos Topológicos de Conjuntos Semialgébricos e o Lema da Estrutura Cônica Local.Geometria algébrica realConjuntos semialgébricosReal algebraic geometrySemi-algebraic setsConjuntos semialgébricos e o teorema da finitude topológicaSemialgebraic sets and the topological finitude theoreminfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessORIGINAL2022_dis_adtanure.pdf2022_dis_adtanure.pdfdissertaçao andre tanureapplication/pdf613793http://repositorio.ufc.br/bitstream/riufc/68082/3/2022_dis_adtanure.pdf691811c2d579be44a735cfd4162c3ee7MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-82152http://repositorio.ufc.br/bitstream/riufc/68082/4/license.txtfb3ad2d23d9790966439580114baefafMD54riufc/680822022-09-08 11:55:17.43oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2022-09-08T14:55:17Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv Conjuntos semialgébricos e o teorema da finitude topológica
dc.title.en.pt_BR.fl_str_mv Semialgebraic sets and the topological finitude theorem
title Conjuntos semialgébricos e o teorema da finitude topológica
spellingShingle Conjuntos semialgébricos e o teorema da finitude topológica
Tanure, André Dantas
Geometria algébrica real
Conjuntos semialgébricos
Real algebraic geometry
Semi-algebraic sets
title_short Conjuntos semialgébricos e o teorema da finitude topológica
title_full Conjuntos semialgébricos e o teorema da finitude topológica
title_fullStr Conjuntos semialgébricos e o teorema da finitude topológica
title_full_unstemmed Conjuntos semialgébricos e o teorema da finitude topológica
title_sort Conjuntos semialgébricos e o teorema da finitude topológica
author Tanure, André Dantas
author_facet Tanure, André Dantas
author_role author
dc.contributor.author.fl_str_mv Tanure, André Dantas
dc.contributor.advisor1.fl_str_mv Fernandes, Alexandre César Gurgel
contributor_str_mv Fernandes, Alexandre César Gurgel
dc.subject.por.fl_str_mv Geometria algébrica real
Conjuntos semialgébricos
Real algebraic geometry
Semi-algebraic sets
topic Geometria algébrica real
Conjuntos semialgébricos
Real algebraic geometry
Semi-algebraic sets
description We present the definition of a semialgebraic subset of Rn, that is a subset defined by a boolean condition of polynomial conditions. We show the first structure theorem for semialgebraic sets, The Cylindrical Decomposition Theorem and explore some of its consequences, in particular the Tarski-Seidenberg Theorem. Then we prove the second structure theorem, The Stratifi cation Theorem. After that, we explore some of its consequences, in particular the concept of dimension, and a version of Sard’s Theorem for semialgebraic mappings. We then present the concepts of Cell Decomposition and Triangulation of a set, and we prove that every compact semialgebraic set admits both a cell decomposition and a triangulation. We then enunciate the Local Triviality Theorem and present two applications: The Theorem on the Finiteness of Topological Types of semialgebraic sets, and the Local Conical Structure Lemma.
publishDate 2022
dc.date.accessioned.fl_str_mv 2022-09-08T14:55:17Z
dc.date.available.fl_str_mv 2022-09-08T14:55:17Z
dc.date.issued.fl_str_mv 2022-08-11
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv TANURE, André Dantas. Conjuntos semialgébricos e o teorema da finitude topológica. 2022. 71 f. Dissertação (Mestrado Acadêmico em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2022.
dc.identifier.uri.fl_str_mv http://www.repositorio.ufc.br/handle/riufc/68082
identifier_str_mv TANURE, André Dantas. Conjuntos semialgébricos e o teorema da finitude topológica. 2022. 71 f. Dissertação (Mestrado Acadêmico em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2022.
url http://www.repositorio.ufc.br/handle/riufc/68082
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dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
instname:Universidade Federal do Ceará (UFC)
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instname_str Universidade Federal do Ceará (UFC)
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reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
collection Repositório Institucional da Universidade Federal do Ceará (UFC)
bitstream.url.fl_str_mv http://repositorio.ufc.br/bitstream/riufc/68082/3/2022_dis_adtanure.pdf
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