\begin{definition}[Definition:Relatively Prime Integer Topology]
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'''.
\end{definition}