A superposition theorem for unbounded continuous functions

Author:
Raouf Doss

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

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Abstract: Let be the *n*-dimensional Euclidean space. We prove that there are 4*n* real functions continuous on with the following property: Every real function *f*, not necessarily bounded, continuous on , can be written , where *g, h* are 2 real continuous functions of one variable, depending on *f*.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1977-0582781-1

Keywords:
Superposition of functions,
several variables,
Hilbert Problem 13

Article copyright:
© Copyright 1977
American Mathematical Society