{"id":{"repo_id":"brazil-ufpb","oai_identifier":"oai:repositorio.ufpb.br:123456789/367"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-ufpb/oai:repositorio.ufpb.br:123456789/367","repository":{"repo_id":"brazil-ufpb","name":"Brazil UFPB","base_url":"https://repositorio.ufpb.br/oai/request"},"display":{"title":"O grau topológico de Brouwer e Aplicações.","abstract":"In this work, we study the Brouwer topological degree theory. first, we study some results about analysis in rn, which are important tools on the study of the degree. after that, we associate each triple (f,⌦, y), where ⌦ ⇢ rn,y 2 rn and f a continuous function in ⌦, to a integer number d(f,⌦, y). this function, known as degree, through its properties and consequences, allows us to find meaningful answers about the existence, uniqueness or multiplicity of solutions for the equation f(x) = y. after that, we construct such a function and study some applications of the theory developed. among them, the Brouwer fixed point theorem.","abstract_html":"In this work, we study the Brouwer topological degree theory. first, we study some results about analysis in rn, which are important tools on the study of the degree. after that, we associate each triple (f,⌦, y), where ⌦ ⇢ rn,y 2 rn and f a continuous function in ⌦, to a integer number d(f,⌦, y). this function, known as degree, through its properties and consequences, allows us to find meaningful answers about the existence, uniqueness or multiplicity of solutions for the equation f(x) = y. after that, we construct such a function and study some applications of the theory developed. among them, the Brouwer fixed point theorem.","abstract_has_math":false,"creators":["Melo Júnior, José Carlos de Albuquerque."],"institution":"Matemática","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-07-08","date_published":"2013-07-08","updated_at":"2026-07-24T01:17:51Z","subjects":["Ensino e aprendizagem da matemática","Análise vetorial","Grau topológico de Brouwer","Teaching and learning mathematics","Vector analysis","Brouwer topological grade"],"languages":["pt"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repositorio.ufpb.br/jspui/handle/123456789/367","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Melo Júnior, José Carlos de Albuquerque."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-07-08T19:02:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-07-08T19:02:30Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-07-08"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Matemática"]},{"key":"dc:type","label":"Dc Type","values":["TCC"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Ensino e aprendizagem da matemática","Análise vetorial","Grau topológico de Brouwer","Teaching and learning mathematics","Vector analysis","Brouwer topological grade"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["pt"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repositorio.ufpb.br/jspui/handle/123456789/367"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work, we study the Brouwer topological degree theory. first, we study some results about analysis in rn, which are important tools on the study of the degree. after that, we associate each triple (f,⌦, y), where ⌦ ⇢ rn,y 2 rn and f a continuous function in ⌦, to a integer number d(f,⌦, y). this function, known as degree, through its properties and consequences, allows us to find meaningful answers about the existence, uniqueness or multiplicity of solutions for the equation f(x) = y. after that, we construct such a function and study some applications of the theory developed. among them, the Brouwer fixed point theorem."]},{"key":"dc:title","label":"Title","values":["O grau topológico de Brouwer e Aplicações."]}]}],"canonical_facts":{"dc:creator":["Melo Júnior, José Carlos de Albuquerque."],"dc:date.accessioned":["2013-07-08T19:02:30Z"],"dc:date.available":["2013-07-08T19:02:30Z"],"dc:date.issued":["2013-07-08"],"dc:description.abstract":["In this work, we study the Brouwer topological degree theory. first, we study some results about analysis in rn, which are important tools on the study of the degree. after that, we associate each triple (f,⌦, y), where ⌦ ⇢ rn,y 2 rn and f a continuous function in ⌦, to a integer number d(f,⌦, y). this function, known as degree, through its properties and consequences, allows us to find meaningful answers about the existence, uniqueness or multiplicity of solutions for the equation f(x) = y. after that, we construct such a function and study some applications of the theory developed. among them, the Brouwer fixed point theorem."],"dc:identifier.uri":["https://repositorio.ufpb.br/jspui/handle/123456789/367"],"dc:language.iso":["pt"],"dc:publisher.department":["Matemática"],"dc:subject":["Ensino e aprendizagem da matemática","Análise vetorial","Grau topológico de Brouwer","Teaching and learning mathematics","Vector analysis","Brouwer topological grade"],"dc:title":["O grau topológico de Brouwer e Aplicações."],"dc:type":["TCC"]},"updated_at":"2026-07-24T01:17:51Z"}