Reducing multi-variable functions to a composition of 1- or 2-variable functions

complex-analysis real-analysis calculus multivariable-calculus special-functions

Solution 1:

I found an answer for essentially the same question asked earlier at MathOverflow.

TL;DR

There exist analytic functions $f$ of 3 variables such that they cannot be represented as a composition of continuously differentiable functions of two variables. The general problem in the class $C^\infty$ seems to be still open.

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