3. Let Y and Z be countable dense subsets of the real line, with the subspace topology (dense means that each open interval contains points of Y and points of Z) . a) Prove that there is an order-preserving bijection f : Y - Z. b) Prove that such an f is continuous, and in fact a homeomorphism. (It is enough to prove at each y E Y that f is continuous at y from the right and from the left.)