Prove that Cantor set is a perfect set.
Google is your friend.
For example, I found this very quickly:
Ok but still that proof is missing a part
Note that this proof is not yet complete. One still has to prove the assertion that each set A n is indeed comprised of 2 n closed subintervals, with all endpoints being part of the Cantor set. But that is left as an exercise.
How to SHOW thaT?