$B \subset \mathbb{R^3}$, such that $B = \rm{Fr} (\Omega)$

Question

$B \subset \mathbb{R^3}$, such that $B = \rm{Fr} (\Omega)$

Where $\Omega = \{(x,y,z) : z \leq 1\}$ and $\rm{Fr}(\Omega)$ means the $\Omega$'s boundary.

Answer 1

I think you're asking "What's the frontier of the subset of $R^3$ consisting of all points whose $z$-coordinates are no more than $1$?"

The answer is $$B = \{(x, y, 1) : x, y \in {\mathbf R} \}$$.

Answer 2

Let $B = (\mathbb{Q}\times\mathbb{Q}\times\mathbb{Q}) \cap \Omega$.