This note is purely expository. We show how in the course of the
Kolmogorov-Arnold solution of Hilbert's 13-th problem on superpositions there
appeared the notion of a basic embedding. A subset K of R^2 is {\it basic} if
for each continuous function f:K->R there exist continuous functions g,h:R->R
such that f(x,y) = g(x) + h(y) for each point (x,y) in K. We present
descriptions of basic subsets of the plane and graphs basically embeddable into
the plane (solutions of Arnold's and Sternfeld's problems).