Open Unit Interval on Rational Number Space is Bounded but not Compact

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

Then:
 * $\openint 0 1 \cap \Q$ is totally bounded but not compact

where $\openint 0 1$ is the open unit interval.

Proof
From the Heine-Borel Theorem on a metric space, $\openint 0 1 \cap \Q$ is compact it is both totally bounded and complete.

From Rational Number Space is not Complete Metric Space it follows that $\openint 0 1 \cap \Q$ is not compact.