摘要
Given any infinite tree in the plane satisfying certain topological conditions,we construct an entire function f with only two critical values±1 and no asymptotic values such that f-1([-1,1])is ambiently homeomorphic to the given tree.This can be viewed as a generalization of the result of Grothendieck(see Schneps(1994))to the case of infinite trees.Moreover,a similar idea leads to a new proof of the result of Nevanlinna(1932)and Elfving(1934).
