The standard topology on the set of residues modulo n

Question

I want to define a topology on the set of residue modulo $p$, $\mathbb{Z}_p$. what is the standard topology on that set?

Answer 1

Usually we have for each group $\Bbb{Z}/n\Bbb{Z}$, with $n\in \Bbb{N}$, the discrete topology (for the $p$-adic integers $\Bbb{Z}_p$, it is the $p$-adic topology, where $p$ is prime).

Answer 2

It's a finite set; I'd say that a typical topology is the discrete topology. That's certainly the one that comes up in the fibration $z \mapsto z^p$ over the unit circle.