Complex numbers - hurwitz theorem

[hermanni]

Hi all,
I'm trying to solve this question , can anyone help??
Suppose that D is an open connected set , fn ->f uniformly on compact subsets of D. If f is nonconstant and z in D , then there exists N and a sequence zn-> z such that
fn ( zn ) = f(z) for all n > N.

hint: assume that f(z) = 0. Apply Hurwitz theorem to in disk D(z0 , rj ) for a suitable sequence of rj -> 0

I reallt don't have an idea and I don't understand how to use hint.Can anyone give a hint??

 

[ystael]

Do you understand what Hurwitz's theorem tells you in this context?

 

[hermanni]

Actually I didn't . The theorem says fn and f have the same number of zeroes, I don't understand how we supposed to use it.