$A=\{(x,y) \in \mathbb{R}^2 \, | \, y \ge 1\}$.

I can see that $A=\mathbb{R}^2 - \{(x,y) \in \mathbb{R}^2 \, | \, y < 1\}$, but then the question is is $U=\{(x,y) \in \mathbb{R}^2 \, | \, y < 1\}$ open? I think it is since it seems possible to find open balls around each point that are contained in the set.