Geodesic
Adic Topologies for the Rational Integers
Canadian journal of mathematics, Tome 55 (2003) no. 4, pp. 711-723

Voir la notice de l'article provenant de la source Cambridge University Press

A topology on $\mathbb{Z}$ , which gives a nice proof that the set of prime integers is infinite, is characterised and examined. It is found to be homeomorphic to $\mathbb{Q}$ , with a compact completion homeomorphic to the Cantor set. It has a natural place in a family of topologies on $\mathbb{Z}$ , which includes the $p$ -adics, and one in which the set of rational primes $\mathbb{P}$ is dense. Examples from number theory are given, including the primes and squares, Fermat numbers, Fibonacci numbers and $k$ -free numbers.
DOI : 10.4153/CJM-2003-030-3
Mots-clés : 11B05, 11B25, 11B50, 13J10, 13B35, p-adic, metrizable, quasi-valuation, topological ring, completion, inverse limit, diophantine equation, prime integers, Fermat numbers, Fibonacci numbers 
Broughan, Kevin A. Adic Topologies for the Rational Integers. Canadian journal of mathematics, Tome 55 (2003) no. 4, pp. 711-723. doi: 10.4153/CJM-2003-030-3
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