- Thread starter
- #1

- Mar 10, 2012

- 834

Now here's what I think can be useful in solving the problem.

Let $V$ be open in $Y$. Then $f^{-1}(V)=\bigcup_{i=1}^{i=\infty}{f|A_i}^{-1}(V)$, where each inverse image in the RHS is open in its corresponding restricted space.

I can't see how to go further. Please help.