# Math Help - bounded,open,closed or connected?

1. ## bounded,open,closed or connected?

Hey. This was a question I came across. What is the right answer?

If A and B are subsets of the Euclidean space,
and A + B ={x + y | x Є A and y Є B}. Then which of the following statements is false?

a) If A and B are bounded, then A + B is bounded
b) If A and B are closed, then A + B is closed
c) If A and B are open, then A + B is open
d) If A and B are connected, then A + B is connected.

I think options (a) and (b) are right. I am not so sure about openness and connectedness..

2. all are right except (b).

3. Originally Posted by Shanks
all are right except (b).
Oh can you tell me how b is wrong?

4. A counterexample: Let N be the set of all positive integers.
A=N, $B=\left\{\frac{1}{n}-n: n\in N, 2\le n\right\}$
A, and B are closed, but A+B has 0 as a cluster point, and 0 is not contained in A+B.