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Sets of range uniqueness for classes of continuous functions

1999
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Proceedings of the American Mathematical Society
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Diamond, Pomerance and Rubel (1981) proved that there are subsets M of the complex plane such that for any two entire functions f and g if f [M ] = g[M], then f = g. Baraducci and Dikranjan showed in 1993 that the continuum hypothesis (CH) implies the existence of a similar set M ⊂ R for the class Cn(R) of continuous nowhere constant functions from R to R, while it follows from the results of Burke and Ciesielski (1997) and Ciesielski and Shelah that the existence of such a set is not provable

doi:10.1090/s0002-9939-99-04905-9
fatcat:i2rk3vutxje35jorbme2v53fii