## A superposition theorem for unbounded continuous functions

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- by Raouf Doss PDF
- Trans. Amer. Math. Soc.
**233**(1977), 197-203 Request permission

## Abstract:

Let ${R^n}$ be the*n*-dimensional Euclidean space. We prove that there are 4

*n*real functions ${\varphi _q}$ continuous on ${R^n}$ with the following property: Every real function

*f*, not necessarily bounded, continuous on ${R^n}$, can be written $f(x) = \Sigma _{q = 1}^{2n + 1}g({\varphi _q}(x)) + \Sigma _{q = 2n + 2}^{4n}h({\varphi _q}(x)),x \in {R^n}$, where

*g, h*are 2 real continuous functions of one variable, depending on

*f*.

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## Additional Information

- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**233**(1977), 197-203 - MSC: Primary 26A72
- DOI: https://doi.org/10.1090/S0002-9947-1977-0582781-1
- MathSciNet review: 0582781