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## Homework Statement

Given A and B are closed sets in R does it follow that A+B is closed? (A+B={a+b|a in A and b in B})

## Homework Equations

A set X is closed iff all of its limiting points are in X.

## The Attempt at a Solution

I don't think this is true. I've tried constructing convergent sequences A and B and having the limit of the sum not being contained in A+B. But then A and B can't be closed.