I can't solve the following problem.
Let $A = \{(x; y) \in \mathbb{R}^2 \mid \max\{|x|, |y|\} \leq 1\}$ and $B = \{(0; y) \in \mathbb{R}^2 \mid y \in \mathbb{R}\}$. Show that the set $A + B = \{a + b \mid a \in A; b \in B\}$ is a closed subset of $\mathbb{R}^2$.
please help anyone.