A superposition theorem of Kolmogorov type for bounded continuous functions

Let C(Rn) denote the set of real valued continuous functions defined on Rn. We prove that for every n≥2 there are positive numbers λ1,…,λn and ϕ1,…,ϕm∈C(R) with following property: bounded f∈C(Rn) is a function g∈C(R) such f(x)=∑q=1mg∑p=1nλpϕq(xp) x=(x1,…,xn)∈Rn. Consequently, can be obtained from one variable using compositions additions.