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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A superposition theorem for bounded continuous functions


Author: Stephen Demko
Journal: Proc. Amer. Math. Soc. 66 (1977), 75-78
MSC: Primary 26A72
MathSciNet review: 0457651
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Abstract: It is shown that there exist $ 2n + 1$ real valued, continuous functions $ {\phi _0}, \ldots ,{\phi _{2n}}$ defined on $ {{\mathbf{R}}^n}$ such that every bounded real valued continuous function on $ {{\mathbf{R}}^n}$ is expressible in the form $ \Sigma _{i = 0}^{2n}g \circ {\phi _i}$ for some $ g \in C({\mathbf{R}})$. Extensions to some unbounded functions are also made.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0457651-5
PII: S 0002-9939(1977)0457651-5
Keywords: Kolmogorov superposition theorem, Baire category theorem
Article copyright: © Copyright 1977 American Mathematical Society