# Functional analysis: are there no true functions with real values ​​of two or more variables?

I see the following theorem somewhere, without complete proof.

For each irrational number $$lambda$$, there are continuous functions $$phi_k: (0,1) to mathbb R, k = 1,2,3,4,5$$, so that for all continuous functions $$f: (0,1) ^ 2 to mathbb R$$, there is a continuous function $$g: (0,1) a mathbb R$$such that $$f (x, y) = sum_ {k = 1} ^ 5 g ( phi_k (x) + lambda phi_k (y))$$.

There are some mysterious things about this result. Where does the number come from? $$5$$ come and why $$lambda notin mathbb Q$$?

Could anyone offer a reference for proof of this?