Superposition stetiger Abbildungen (Q1062161)

The Kolmogorov theorem on the representation of any real continuous function f on the unit square \(I^ 2\) by superposition of 5 real continuous functions of one variable and addition is generalized to continuous functions f on \(I^ 2\) taking values in a complete p-normed vector space \(X_ p,\quad 0<p\leq 1.\) (The unusual p-norm in such a space satisfies \(\| ax\| \leq | \alpha |^ p\| x\|.)\) The number m of summands increases from 5 to at least \(2+3^{1/p}\).