Suppose we have a continuous function $f:R^2\rightarrow R$. I was told of the following remarkable theorem: $f$ can be expressed as the composition of continuous unary functions (that is, functions from $R\rightarrow R$) and addition.


Could anyone give me a reference (or name) for this theorem?



Expressing any f(x,y) using only addition and unary functions?
This is "due in successively more exact forms to Kolmogorov, Arnol'd and a succession of mathematicians ending with Kahane", to quote T.W. Korner on the subject.


I am informed that the proof I met is prepared using:


J.-P. Kahane *Sur le treizieme probleme de Hilbert, le theoreme de superposition de Kolmogorov et les sommes algebriques d'arcs croissants* in the conference proceedings *Harmonic analysis, Iraklion 1978* Springer 1980


G. G. Lorenz, *Approximation of functions* Chelsea Publishing Co. 1986 (First Ed. 1966)


A. G. Vituskin *On the representation of functions by superpositions and related topics* in L'Enseignement Mathématique, 1977, Vol 23, pages 255-320


[This is all from these skeleton notes (no proofs) [here](http://www.dpmms.cam.ac.uk/~twk/CV4.pdf) (Links to pdf; See Chapter 1 and Chapter 11 for references)]


