  We discuss subsets $S$ of ${\mathbb{R}}^n$ such that every real valued
function $f$ on $S$ is of the form {equation*} f(x_1,x_2,...,x_n) = u_1(x_1) +
u_2(x_2) + ... + u_n(x_n), {equation*} and the related concepts and situations
in analysis.
