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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
-
Paul Erdös and Arthur H. Stone, On the sum of two Borel sets, Notices Amer. Math. Soc. 16 (1969), 968-969. Abstract #69T-B175.
- R. Purves, Bimeasurable functions, Fund. Math. 58 (1966), 149–157. MR 199339, DOI https://doi.org/10.4064/fm-58-2-149-157
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 04.40
Retrieve articles in all journals with MSC: 04.40
Additional Information
Keywords:
Borel set,
homeomorphism,
real numbers
Article copyright:
© Copyright 1970
American Mathematical Society