Definition:Relatively Prime Integer Topology

Definition
Let $\Z_{>0}$ denote the set of (strictly) positive integers.

Let $\BB$ be the set of sets $\set {\map {U_a} b: a, b \in \Z_{>0} }$ where:
 * $\map {U_a} b = \set {b + n a \in \Z_{>0}: \gcd \set {a, b} = 1}$

where $\gcd \set {a, b}$ denotes the greatest common divisor of $a$ and $b$.

Then $\BB$ is the basis for a topology $\tau$ on $\Z_{>0}$.

$\tau$ is then referred to as the relatively prime integer topology.

The topological space $T = \struct {\Z_{>0}, \tau}$ is referred to as the relatively prime integer space.

Also known as
While you would expect the relatively prime integer topology to be known as the coprime integer topology, apparently it is not.

Also see

 * Relatively Prime Integer Topology is Topology