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arXiv · 0809.4733

Spaces with a Finite Family of Basic Functions

Paul Gartside·Feng Ziqin
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Abstract

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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Paul Gartside, Feng Ziqin. 2008-09-27. Spaces with a Finite Family of Basic Functions. https://doi.org/10.1112/blms%2Fbdq077

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