Irrational Number Space is not Weakly Sigma-Locally Compact

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

Then $\struct {\R \setminus \Q, \tau_d}$ is not weakly $\sigma$-locally compact.

Proof
From Irrational Number Space is not Locally Compact Hausdorff Space, $\struct {\R \setminus \Q, \tau_d}$ is not weakly locally compact.

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