N. Aronszajn proved [Ann. Math., II. Ser. 43, 730-738 (1942; Zbl 0061.171)] that the set S of solutions of the initial value problem \(x'=f(t,x)\), \(x(0)=x_ 0\) where \(x\in {\mathbb{R}}^ n\), \(t\in I=[0,T]\) and f is bounded and continuous on \(I\times {\mathbb{R}}^ n\), is a \(R_{\delta}\)-set in the space C(I) of continuous functions from I into \({\mathbb{R}}^ n\) that means, S is the intersection of a decreasing sequence of compact absolute retracts. The authors of this note extend the mentioned result to the set of solutions of the differential inclusion x’\(\in F(t,x)\), \(x(0)=0\) where F is a set-valued function whose values are nonempty, compact, convex subsets of \({\mathbb{R}}^ n\) and F is assumed to be bounded and upper semicontinuous.