Definition:Furstenberg Topology

Definition
Let $\Z$ be the set of integers.

Let:
 * $\BB := \set { a \Z + b : a,b \in \Z, a \ne 0 }$

where:
 * $a\Z + b := \set {a k + b : k \in \Z }$

Furstenberg topology is the topology on $\Z$ generated by the synthetic basis $\BB$.