Spaces with a Finite Family of Basic Functions
Abstract
A space X is finite dimensional, locally compact and separable metrizable if and only if X has a finite basic family: continuous functions Phi1,...,Phin of X to the reals, R, such that for all continuous f from X to R there are g1,..., gn in C(R) satisfying f(x)=g1(Phi1(x))+g2(Phi2(x))+...+gn(Phin(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.
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