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arXiv · 1008.0713

On an exotic topology of the integers

Rezsö L. Lovas·István Mezö
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Abstract

We study some interesting properties of Furstenberg's topology of the integers. We show that it is metrizable, totally disconnected, and (Z,+,.) is a topological ring with respect to this topology. As an application, we show that any two disjoint sets of primes can be separated by arithmetic progressions.

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Rezsö L. Lovas, István Mezö. 2010-08-04. On an exotic topology of the integers. https://arxiv.org/abs/1008.0713

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