Entire functions with prescribed singular values

We introduce a new class of entire functions epsilon which consists of all F-0 is an element of O(C) for which there exists a sequence (F-n) is an element of O(C) and a sequence (lambda(n)) is an element of C satisfying F-n(z) = lambda(n+1)e(Fn+)1((z)) for all n >= 0. This new class is closed under the composition and it is dense in the space of all nonvanishing entire functions. We prove that every closed set V subset of C containing the origin and at least one more point is the set of singular values of some locally univalent function in epsilon, hence, this new class has nontrivial intersection with both the Speiser class and the Eremenko-Lyubich class of entire functions. As a consequence, we provide a new proof of an old result by Heins which states that every closed set V subset of C is the set of singular values of some locally univalent entire function. The novelty of our construction is that these functions are obtained as a uniform limit of a sequence of entire functions, the process under which the set of singular values is not stable. Finally, we show that the class epsilon contains functions with an empty Fatou set and also functions whose Fatou set is nonempty.