I'm trying to figure out a problem here and I don't quite get it.
Let be a bijection between and . For , define to be the open set -ball around the point . Define . Show that F is compact.
Now I don't want the answer to this question; I want to figure it out. It's just that I could swear that the set is empty, which I know is compact. However, the next part of the question asks me to show that and that .
Basically, it looks to me like completely engulfs and then some, so wouldn't contain any values. Thus the set F is empty.
Please Help! Thank you very much.