Unifying the little Picard, Lohwater–Pommerenke and Brody theorems

A theorem unifying the theorems of little Picard, Lohwater–Pommerenke and Brody is presented: Let M,Y be complex spaces. Then a family of holomorphic maps F⊂H(M,Y) is uniformly normal iff every F-limiting curve is trivial. Furthermore, Zalcman's lemma and the Robinson–Zalcman Heuristic Principle are ‘extended.’