Rational Number Space is not Weakly Sigma-Locally Compact

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Theorem

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


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


Proof

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

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

$\blacksquare$


Sources