Coset topology
The set is $\mathbb{Z}$. A subset $ X $ is open if $\forall b \in X:\exists a \in \mathbb{Z}_{>0}: b+a\mathbb{Z} \subset X$.
The set is $\mathbb{Z}$. A subset $ X $ is open if $\forall b \in X:\exists a \in \mathbb{Z}_{>0}: b+a\mathbb{Z} \subset X$.