Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.