I understand this question can be done by using the fact that the intersection of closed sets is closed. However, i'm assuming you could also use De Morgan's Law and show that the complement of the cantor set is open (union of open sets) hence the cantor set is closed? (Both Instances requiring induction of course)
Best Answer
Yes, intersections of closed subsets of a space are also closed. This can be derived (using De Morgan's Law) from the fact (or rather axiom of a topology) that unions of open subsets are also open. There is no need to give a special argument in the case of the Cantor set. This follows immediately from the general fact.