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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Nomographic functions are nowhere dense


Author: R. Creighton Buck
Journal: Proc. Amer. Math. Soc. 85 (1982), 195-199
MSC: Primary 41A63; Secondary 41A30
DOI: https://doi.org/10.1090/S0002-9939-1982-0652441-4
MathSciNet review: 652441
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Abstract: A function $ f$ of $ n$ variables is nomographic if it can be represented in the format

$\displaystyle f({x_1}, \ldots ,{x_n}) = h({\phi _1}({x_1}) + \cdots + {\phi _n}({x_n}))$

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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0652441-4
Keywords: Superpositions, Hilbert, nowhere dense
Article copyright: © Copyright 1982 American Mathematical Society

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