If is closure of A, you should have proved that for continuous mapping, .
From the given you know that .
Now finish it off.
Let be a continuous map of topological spaces.
1) Let A and B be subsets of X such that the closure of A = closure of B. Prove that the closure of f(A) = closure of f(B).
2) Prove that if A is dense in X and f(X)is dense in Y then f(A) is dense in Y.
These both look fairly self-intuitive but how can we actaully prove them?
OK thanks for your help. Fair point but sometimes it's difficult knowing if you're on the right track at all and so writing down "how far you've got" may just be an assortment of completely irrelevant ideas. I don't see however how this proves part 2 of the question, and as far as I can see I'm not missing anything obvious either...