\begin{definition}[Definition:Divisor Topology]
Let $S = \set {x \in \Z: x \ge 2}$ denote the set of integers greater than $1$.
Let $\BB$ be the set of all sets $U_n$ defined for all $n \ge 2$ as:
:$U_n = \set {x \in \Z_{>0}: x \divides n}$
where $\divides$ denotes the divisor relation.
Then $\BB$ is the basis for a topology $\tau$ on $S$.
Then $\tau$ is referred to as the '''divisor topology'''.
The topological space $T = \struct {S, \tau}$ is referred to as the '''divisor space'''.
\end{definition}