Suppose there is a question:
How do you prove invariance of domain?
which is answered in a complete, elementary manner. Now, suppose another question comes along which says:
Supposing the generalized Jordan curve theorem, how do you prove invariance of domain?
Naturally, one way is to ignore the Jordan Curve theorem and prove it in the same manner as the first question but it is clear (to me) that the question expects the use of the Jordan curve theorem in the answer.
Are these questions duplicate? I would have a hard time saying yes. But there are much subtler cases when the new information doesn't necessarily give an advantage. Pretend the elementary proof in the first problem is much simpler than the proof using the Jordan curve theorem. Are they still duplicates? Now, if the Jordan curve theorem were unrelated, it would be a different story. But we are supposing the theorem is related to the problem but the elementary proof is easier.