Originally Posted by

**Amanda1990** Thanks a lot - for the first part of the question I had the right idea but just couldn't write it properly.

For the last point you made, did you mean to use I instead of p? The map p just takes any real number to its equivalence class right? ie isn't $\displaystyle p(x) = [I(x), I(x) +1)$?

On a similar note, I agree that I is not continuous, but I does define a bijection, J say, from $\displaystyle {R}/$~ $\displaystyle \rightarrow Z$ (I think this i fairly clear). What is the topology on Z making J a homomorphism?