Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets
Descripción del Articulo
This article provides a detailed analysis of the relationship between the Cantor-Bendixson derivative and set containment, as well as the standard set operations of union and intersection. In particular, it is shown that the Cantor-Bendixson derivative is increasing with respect to set containment a...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Fecha de Publicación: | 2023 |
| Institución: | Universidad Nacional de Trujillo |
| Repositorio: | Revistas - Universidad Nacional de Trujillo |
| Lenguaje: | español |
| OAI Identifier: | oai:ojs.revistas.unitru.edu.pe:article/5355 |
| Enlace del recurso: | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5355 |
| Nivel de acceso: | acceso abierto |
| Materia: | Derivada de Cantor-Bendixson derivado de un conjunto Cantor-Bendixson derivative derivative of a set |
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Relationship Between the Cantor-Bendixson Derivative and the Algebra of SetsRelación de la Derivada de Cantor-Bendixson con el Álgebra de ConjuntosMerino, AndresHeredia F., SebastiánDerivada de Cantor-Bendixsonderivado de un conjuntoCantor-Bendixson derivativederivative of a setThis article provides a detailed analysis of the relationship between the Cantor-Bendixson derivative and set containment, as well as the standard set operations of union and intersection. In particular, it is shown that the Cantor-Bendixson derivative is increasing with respect to set containment and, under suitable hypotheses, generates a decreasing family of sets. On the other hand, we study both the derivative of a union and the derivative of an intersection, under different restrictions on the cardinality of the family of sets being operated on, while taking into account the order of derivative being performed.En el presente artículo se realiza un análisis a detalle sobre la relación de la derivada de Cantor-Bendixson con la contenencia de conjuntos y las operaciones usuales de conjuntos (unión e intersección). En particular, se demuestra que la derivada de Cantor-Bendixson es creciente con respecto a la contenencia de conjuntos y, bajo hipótesis adecuadas, genera una familia decreciente de conjuntos. Por otro lado, se estudia tanto el derivado de una unión, como de una intersección, bajo diferentes restricciones en la cardinalidad de la familia de conjuntos a operar y tomando en cuenta el orden de derivado a realizar.National University of Trujillo - Academic Department of Mathematics2023-12-27info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/5355Selecciones Matemáticas; Vol. 10 No. 02 (2023): August - December; 339 - 351Selecciones Matemáticas; Vol. 10 Núm. 02 (2023): Agosto - Diciembre; 339 - 351Selecciones Matemáticas; v. 10 n. 02 (2023): Agosto - Dezembro; 339 - 3512411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUspahttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/5355/5798Derechos de autor 2023 Selecciones Matemáticashttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/53552023-12-27T14:40:03Z |
| dc.title.none.fl_str_mv |
Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets Relación de la Derivada de Cantor-Bendixson con el Álgebra de Conjuntos |
| title |
Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets |
| spellingShingle |
Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets Merino, Andres Derivada de Cantor-Bendixson derivado de un conjunto Cantor-Bendixson derivative derivative of a set |
| title_short |
Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets |
| title_full |
Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets |
| title_fullStr |
Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets |
| title_full_unstemmed |
Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets |
| title_sort |
Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets |
| dc.creator.none.fl_str_mv |
Merino, Andres Heredia F., Sebastián |
| author |
Merino, Andres |
| author_facet |
Merino, Andres Heredia F., Sebastián |
| author_role |
author |
| author2 |
Heredia F., Sebastián |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Derivada de Cantor-Bendixson derivado de un conjunto Cantor-Bendixson derivative derivative of a set |
| topic |
Derivada de Cantor-Bendixson derivado de un conjunto Cantor-Bendixson derivative derivative of a set |
| description |
This article provides a detailed analysis of the relationship between the Cantor-Bendixson derivative and set containment, as well as the standard set operations of union and intersection. In particular, it is shown that the Cantor-Bendixson derivative is increasing with respect to set containment and, under suitable hypotheses, generates a decreasing family of sets. On the other hand, we study both the derivative of a union and the derivative of an intersection, under different restrictions on the cardinality of the family of sets being operated on, while taking into account the order of derivative being performed. |
| publishDate |
2023 |
| dc.date.none.fl_str_mv |
2023-12-27 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5355 |
| url |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5355 |
| dc.language.none.fl_str_mv |
spa |
| language |
spa |
| dc.relation.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5355/5798 |
| dc.rights.none.fl_str_mv |
Derechos de autor 2023 Selecciones Matemáticas https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
Derechos de autor 2023 Selecciones Matemáticas https://creativecommons.org/licenses/by/4.0 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
National University of Trujillo - Academic Department of Mathematics |
| publisher.none.fl_str_mv |
National University of Trujillo - Academic Department of Mathematics |
| dc.source.none.fl_str_mv |
Selecciones Matemáticas; Vol. 10 No. 02 (2023): August - December; 339 - 351 Selecciones Matemáticas; Vol. 10 Núm. 02 (2023): Agosto - Diciembre; 339 - 351 Selecciones Matemáticas; v. 10 n. 02 (2023): Agosto - Dezembro; 339 - 351 2411-1783 reponame:Revistas - Universidad Nacional de Trujillo instname:Universidad Nacional de Trujillo instacron:UNITRU |
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Universidad Nacional de Trujillo |
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UNITRU |
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UNITRU |
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Revistas - Universidad Nacional de Trujillo |
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Revistas - Universidad Nacional de Trujillo |
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1845886946925084672 |
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13.377112 |
Nota importante:
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
