Nomographic functions are nowhere dense

Buck, R. Creighton

doi:10.1090/S0002-9939-1982-0652441-4

Nomographic functions are nowhere dense
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by R. Creighton Buck PDF

Proc. Amer. Math. Soc. 85 (1982), 195-199 Request permission

Abstract:

A function $f$ of $n$ variables is nomographic if it can be represented in the format \[ f({x_1}, \ldots ,{x_n}) = h({\phi _1}({x_1}) + \cdots + {\phi _n}({x_n}))\] where the ${\phi _i}$ and $h$ are continuous. Every continuous function of $n$ variables has a representation as a sum of not more than $2n + 1$ nomographic functions [textbf9]. This paser gives a constructive proof that the nomographic functions form a nowhere dense subset of the space $C[{I^n}]$.

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