Can the topological spaces $\mathbb{R}$ and $\mathbb{Q}$ be expressed as a colimit of a diagram of discrete/finite spaces?

Question

I am interested in knowing if $\mathbb{R}$ and $\mathbb{Q}$ are colimits in the category of topological spaces of a diagram $J$ of discrete or finite spaces. I would like to know also if it is possible choosing discrete or finite subspaces of $\mathbb{R}$ or $\mathbb{Q}$. I am interested in the eight cases. If the answer is no, any non-trivial way of expressing $\mathbb{R}$ and $\mathbb{Q}$ as colimits is of interest.

Almost-discrete topological spaces adresses a similar question but the answers do not treat the colimit case.

Answer 1

The functor $\mathbf{Set} \to \mathbf{Top}$ that equips a set with the discrete topology commutes with colimits, because it's left adjoint to the forgetful functor. Thus any colimit of discrete spaces is discrete.