On the analog of the Kolmogorov-Arnold superposition representation for continuous functions of several $p$-adic variables

Abstract

It is shown that any continuous function depending on several $p$-adic variables, each of which is defined on $\mathbb{Z}_{p}$, can be represented as a superposition of continuous functions of one $p$-adic variable. This statement is true for both functions with values in $\mathbb{R}$ and functions with values in $\mathbb{Q}_{p}$.