Relationship Between the Cantor-Bendixson Derivative and the Algebra of Sets

• Autores: Merino, Andres, Heredia F., Sebastián
• 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

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.