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arXiv · 1605.00853

A primitive associated to the Cantor-Bendixson derivative on the real line

Borys Álvarez-Samaniego·Andrés Merino
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Abstract

We consider the class of compact countable subsets of the real numbers $\mathbb{R}$. By using an appropriate partition, up to homeomorphism, of this class we give a detailed proof of a result shown by S. Mazurkiewicz and W. Sierpinski related to the cardinality of this partition. Furthermore, for any compact subset of $\mathbb{R}$, we show the existence of a "primitive" related to its Cantor-Bendixson derivative.

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Borys Álvarez-Samaniego, Andrés Merino. 2016-05-02. A primitive associated to the Cantor-Bendixson derivative on the real line. https://doi.org/10.18642/jmsaa_7100121692

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