Interior of a subset of $\mathbb{R}^3$ where $(x,y)\in\mathbb{Q}^2$

Question

I'm having problems to visualize the interior and accumulation points of this set $$ D = \left\{ (x,y,z)\in\mathbb{R}^3 \; : \; z = 5-x^2-y^2 \geq 0, (x,y) \in \mathbb{Q}\times\mathbb{Q}\right\}\cup \left\{\left(4,4,\frac{1}{n}\right) \; : \; n\in \mathbb{N} \right\} $$

I understand there must be some kind of delimited circle (like a "strainer") on the $XY$ plane, but i'm not sure how to proceed when $x$ and $y$ are rational numbers. Since the density of irrational numbers, is $D^{\mathrm{o}}$ empty?

Answer 1

The set $\mathring D$ is empty, since $D$ is countable (which follows from the fact that $\mathbb Q$ is countable).