You interchanged (a typing mistake I hope) the second and third's answers (the interior of the complement of a dense set is empty).
I have a good idea of how to prove the following statements, I'm just wondering if they are correct.
Basically, letting S = Q x Q (where Q is the set of rational numbers, so S is therefore the Cartesian Product of the set of rational numbers). I've deduced that:
Boundary((Int(S)) = 0
Interior(Complement(S)) = R^2
Boundary(Int(Complement(S))) = 0
Closure(Interior(S)) = 0
Interior(Closure(S)) = R^2
So just need to make sure Im looking at these the right way, and these are correct statements.
Thanks a lot for your help.