We say that a sequence of maps f: (X, dx ) - (Y, dy ) converges point-wise to a map f: (X, dx) - (Y, dy), denoted fn - f, if for all x E X, we have lim fri(x) = f(x). In other words, for any & > 0 and any x E X, there is a positive integer N (note that N depends on both x and &) such that for all n > N we have dy(fn(x), f(x))