Hey guys, I was just thinking of a question in topological group. Suppose A and B are two closed sets in a topological group, then A*B is closed. Can any of you help me think of a counter example of this please? Or, if you think it is true, then you may prove it.
Thanks a lot.
Iondor's example is a lot simpler and neater than the one I gave. But the vector space example shows that you can even take A and B to be closed subgroups of a topological group, and their "product" (which is their sum in this case) can still fail to be closed.