Spaces with a Finite Family of Basic Functions

Details Spaces with a Finite Family of Basic Functions Spaces with a Finite Family of Basic Functions

2008-09-27

arxiv.org/abs/0809.4733v1

Mathematics

Functional Analysis

Scientific paper

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.

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