Suppose that D is a connected set open set , and

uniformly on compact subsets of D. If f is nonconstant and

then there exists N and a sequence such that for all

Hint: Assume that f(z) = 0. Apply the hurwitz theorem in the disk for a suitable sequence

I didn't even understand the hint.hurwitz theorem states that

and f have the same number of the zeroes in the disk. Can anyone help, thanx.