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.