# general topology – Can we prove that \$mathbb{Q} subseteq mathbb{R}\$ is \$T_4\$

Suppose that $$mathbb{Q} subseteq mathbb{R}$$ equipped with the subspace (Euclidean) Topology is a $$T_4$$ space.

So my thoughts go as follows: We know that $$mathbb{Q}$$ is a subspace, so if we can show that $$mathbb{R}$$ is metrizable (I think with the Euclidean topology) then we get that $$mathbb{Q}$$ is $$T_4$$.

If my thought process is correct, do I still need to show that $$mathbb{R}$$ is metrizable w.r.t the Euclidean topology.