A space X is finite dimensional, locally compact and separable metrizable if
and only if X has a finite basic family: continuous functions Phi_1,...,Phi_n
of X to the reals, R, such that for all continuous f from X to R there are
g_1,..., g_n in C(R) satisfying
f(x)=g_1(Phi_1(x))+g_2(Phi_2(x))+...+g_n(Phi_n(x)) for all x in X. This give
the complete solution to four problems on basic functions posed by Sternfeld,
as well as questions posed by Hattori and others

Gartside, Paul