Suppose A and B are nonempty closed bounded subsets of .

1. Show that there exist such that .

2. Show that this is not true if the boundedness condition on and is dropped.

3. What if only one of or is bounded but both are still closed?

Question about #1, if are closed and bounded, does this mean every sequence in is bounded?

Also, I'm clueless about #2 and #3. Some help please.