Summary of Topology on P-adic Numbers

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 $\struct{\Q_p, \tau_p}$ is:
 * $(1) \quad$ Hausdorff
 * $(2) \quad$ second countable
 * $(3) \quad$ totally disconnected
 * $(4) \quad$ locally compact

Proof
Follows from:
 * P-adic Numbers is Hausdorff Topological Space
 * P-adic Numbers is Second Countable Topological Space
 * P-adic Numbers is Totally Disconnected Topological Space
 * P-adic Numbers is Locally Compact Topological Space