Irrational Number Space is not Weakly Sigma-Locally Compact

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 $\sigma$-locally compact.

Proof
From Irrational Number Space is not Locally Compact, $\left({\R \setminus \Q, \tau_d}\right)$ is not weakly locally compact.

Hence the result from definition of $\sigma$-locally compact.