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## Main Question or Discussion Point

We have two closed sets A,B in R^n. Does A+B= {x+y | x is an element of A, y is an element of B} have to be closed?

I know that both the union and intersection of two closed sets have to be closed. I'm guessing from the question that the answer is no, but I've been playing around with different intervals or R^2 sets that could represent A and B and can't come up with any counterexample to show that A+B need not be closed.

Thanks for any help you can offer!

I know that both the union and intersection of two closed sets have to be closed. I'm guessing from the question that the answer is no, but I've been playing around with different intervals or R^2 sets that could represent A and B and can't come up with any counterexample to show that A+B need not be closed.

Thanks for any help you can offer!

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