0
$\begingroup$

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.

  • 5
    What have you tried? You'll be more likely to get helpful responses if you show the work you've done, so that people can see what you understand and where you're getting stuck.2012-09-20
  • 2
    Could you draw this set if asked? What definition of "closed" are you using? If it's "closed sets have open complements," have you thought about the complement of $A+B$ yet?2012-09-20

1 Answers 1