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On the $ 1-1$ sum of two Borel sets


Author: Richard B. Darst
Journal: Proc. Amer. Math. Soc. 25 (1970), 914
MSC: Primary 04.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0263638-1
MathSciNet review: 0263638
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Abstract: It is shown that there exists a Borel subset $ B$ of the real line and a homeomorphism $ \phi $ of the real line such that the set $ \{ x - \phi (x);x \in B\} $ is not a Borel set.


References [Enhancements On Off] (What's this?)

  • [1] Paul Erdös and Arthur H. Stone, On the sum of two Borel sets, Notices Amer. Math. Soc. 16 (1969), 968-969. Abstract #69T-B175.
  • [2] R. Purves, Bimeasurable functions, Fund. Math. 58 (1966), 149–157. MR 0199339

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0263638-1
Keywords: Borel set, homeomorphism, real numbers
Article copyright: © Copyright 1970 American Mathematical Society