A structured proof of the Kolmogorov superposition theorem

Abstract

We present a well-structured detailed exposition of a well-known proof of the following celebrated result solving Hilbert's 13th problem on superpositions. For functions of 2 variables the statement is as follows.Kolmogorov Theorem. There are continuous functions ϕ 1 , . . . , ϕ 5 : [ 0, 1 ] → [ 0, 1 ] such that for any continuous function f :The proof is accessible to non-specialists, in particular, to students familiar with only basic properties of continuous functions.