Let $A$ , $B$ be open subsets of $\mathbb{R}^n$ . Is $A+B$ a open subset of $\mathbb{R}^n$? Same question replacing open sets by compact sets. I know that for closed sets the result is not true.
Regarding sum of subsets of $\mathbb{R}^n$
2
$\begingroup$
general-topology
-
0thanks Moreland . each a+B is open and arbitrary union of open sets is open – 2012-07-08
-
1The compact question can be answered by reading http://math.stackexchange.com/questions/80974/closed-sum-of-sets – 2012-07-08