Can someone teach me how to find interior, exterior and boundary of these two sets in the plane, $\mathbb R^2$? The metric is $d_2 (x,y)=\sqrt{(x_1-y_1)^2 +(x_2-y_2)^2}$, where $x = (x_1, x_2)$ and $y = (y_1, y_2)$.
$A = \{(x,y): xy \neq 0\}$
$B = \{(x,y):x^2+y^2 <1 \text{ and } x,y \in \mathbb Q\}$
It's really confusing to me. Thanks for your help.