Volume no :41, Issue no: 1, September 2016

Journal of Mathematical Sciences: Advances and Applications

A PRIMITIVE ASSOCIATED TO THE CANTOR-BENDIXSON DERIVATIVE ON THE REAL LINE

Author's: Borys Álvarez-Samaniego and Andrés Merino
Pages: [1] - [33]
Received Date: July 15, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121692

Abstract

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

Keywords

Cantor-Bendixson’s derivative, ordinal numbers.