The authors give a proof for the following theorem, which is a result on the approximation of a nonconvex set-valued mapping by a continuous function. Suppose that \(V\subset I\times R^ n\) and that F:V\(\to (non\)- empty compact contractible subsets of \(R^ n\}\) is an upper semicontinuous multiple valued function. Then, for any compact topological polyhedron \(W\subset V\) and any \(\epsilon >0\) there exists a continuous function \(f:W\to R^ n\) such that \(d^ 0[graph(f)\), \(graph(F(W))]<\epsilon\). Here \(d^ 0(A,B)=\sup \{d(v,B)|\) \(v\in A\}\). The proof proceeds by extending f successively in the order of increasing dimension, and uses the contractibility of F(y) for the extensions. \{The paper is marred by a number of minor errors which make it difficult to read.\}