Let $A, B \in E^n$, and consider their sum $A + B = \{x+y \mid x \in A, y \in B\}$. Suppose that $A$ is open and $B$ is closed.
Is it always true that $A+B$ is open?
Is it always true that $A+B$ is closed?
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1What is $E^n$?${}$ – David Mitra Mar 13 '14 at 13:31
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$E^n=\mathbb R^n$? Also what do you have so far? Don't tell me you have no idea on both questions. – user2345215 Mar 13 '14 at 13:33
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2Hint: $A+B=\bigcup_{b\in B}(b+A)$ therefore open. – Yai0Phah Mar 13 '14 at 13:49
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I dont know wat $E^n$ is?this may be a set of intervals!! – armin Mar 13 '14 at 21:23
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Try simple examples. The most basic closed set, for instance, is a point. What happens in this case?
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