A topology on $mathbb{Z}$, which gives a nice proof that theset of prime integers is infinite, is characterised and examined.It is found to be homeomorphic to $mathbb{Q}$, with a compactcompletion homeomorphic to the Cantor set. It has a natural placein 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 theprimes and squares, Fermat numbers, Fibonacci numbers and $k$-freenumbers.
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机译：对$ mathbb {Z} $上的拓扑进行了特征描述并对其进行了检验，它很好地证明了质数整数的集合是无穷大的。它发现与$ mathbb {Q} $是同胚的，而紧凑补全对Cantor集是同胚的。它在$ mathbb {Z} $上的一系列拓扑中占有一席之地，其中包括$ p $ -adics，以及其中有理素数$ mathbb {P} $密集的拓扑。给出了数论的例子，包括素数和平方，费马数，斐波那契数和$ k $ -freenumbers。
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