A Categorical Construction of Ultrafilters

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Ultrafilters are useful mathematical objects having applications in nonstandard analysis, Ramsey theory, Boolean algebra, topology, and other areas of mathematics. In this note, we provide a categorical construction of ultrafilters in terms of the inverse limit of an inverse family of finite partitions; this is an elementary and intuitive presentation of a consequence of the profiniteness of Stone spaces. We then apply this construction to answer a question of Rosinger posed in arXiv:0709.0084v2 in the negative.
5 pages

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Category Theory, General Mathematics, General Topology, 54D80 (Primary); 16B50 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/230014

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.2497
 http://arxiv.org/abs/0710.2497

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arXiv