Definition:Divisor Topology

Definition
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.

Also see

 * Divisor Topology is Topology