Irrational Number Space is not Locally Compact Hausdorff Space

Theorem
Let $\left({\R \setminus \Q, \tau_d}\right)$ be the irrational number space under the Euclidean topology $\tau_d$.

Then $\left({\R \setminus \Q, \tau_d}\right)$ is not a locally compact Hausdorff Space.