Definition:P-adic Topology

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

Let $p \in \Z$ be a fixed prime number.

Let $\BB$ be the set of all sets $\map {U_\alpha} n$ defined as:
 * $\map {U_\alpha} n = \set {n + \lambda p^\alpha: \lambda \in \Z}$

Then $\BB$ is the basis for a topology $\tau$ on $S$.

$\tau$ is referred to as the $p$-adic topology (on $\Z$).

The topological space $T = \struct {S, \tau}$ is referred to as the $p$-adic (topological) space.

Also see

 * $p$-adic Topology is Topology