On an exotic topology of the integers

Details On an exotic topology of the integers On an exotic topology of the integers

2010-08-04

arxiv.org/abs/1008.0713v1

Mathematics

General Topology

6 pages

Scientific paper

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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