P-adic Numbers is Totally Disconnected Topological Space

Theorem
Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.

Let $\tau_p$ be the topology induced by the non-Archimedean norm $\norm {\,\cdot\,}_p$.

Then the topological space $\struct {\Q_p, \tau_p}$ is totally disconnected.

Proof
From P-adic Numbers form Non-Archimedean Valued Field:
 * $\norm {\,\cdot\,}_p$ is a non-Archimedean norm.

From Non-Archimedean Division Ring is Totally Disconnected:
 * $\struct {\Q_p, \tau_p}$ is totally disconnected.