Let $n\geq 1$ be an integer and suppose $S\subseteq {\mathbb R}^n$ is countable and dense. Do we have $S \cong {\mathbb Q}^n$ where both sets carry the topology inherited from the Euclidean topology on ${\mathbb R}^n$?



Are countable dense subspaces of $\mathbb{R}^n$ homeomorphic to ${\mathbb Q}^n$?
According to <https://arxiv.org/abs/1210.1008>
Example 2(c)... yes, they are all homeomorphic to $\mathbb Q$!


