I'm not very good at topology but am reviewing it for the GRE Subject Test. Here's a question that I think I know, but would like to check with you guys. We define: Ek = B(0, k) - B(0, k-1), where B(0,k) is an open ball around the origin with diameter k. Now suppose that Tk is a subset of Ek for all k, where T is compact. Now let K be the union (1 to infinity) of all Tk. Is K open or closed? I say closed, but I'm not sure.