Rational Numbers are Totally Disconnected/Proof 2

Theorem

Let $\struct {\Q, \tau_d}$ be the rational number space under the Euclidean topology $\tau_d$.

Then $\struct {\Q, \tau_d}$ is a totally disconnected space.

Proof

Follows from:

Rational Number Space is Totally Separated

Totally Separated Space is Totally Disconnected

$\blacksquare$