## Can a projection be approximated by certain symmetric functions?

Hi all.

I'm not a mathematician and will appreciate any help to this.

Suppose and algebra of functions generated by the constant 1 and symmetric functions of three variables (excluded those such that the variables have power one) is dense in the set of continuous functions on a compact product space (e.g. $\displaystyle [a,b]^3$).
How can the coordinate projection (i.e. $\displaystyle p_2(x,y,z)=y$) be approximated by products and linear combinations of those symmetric functions?

thanks