Let
$A=\{(x, y)\in\mathbb R^2 :|x|\leq2\}$
$B=\{(x, y)\in\mathbb R^2 :0 <x+y <2\}$
$C$ is the intersection of $A$ and $B$
I have to write down the closure of $C$ in set notation for the metric
$d ( (x, y), (w, z))=|x-w|+d_{0}(y, z)$
Not sure how to go about this. My limited knowledge of closure is turning inequalities to strict inequalities. I think I just need all points that I can put a ball around for all radius lengths that lie in $C$, but cant imagine what these points are or balls look like.
Thank for any help