English

Sets with distinct sums of pairs, long arithmetic progressions, and continuous mappings

Classical Analysis and ODEs 2018-09-19 v2

Abstract

We show that if φ ⁣:RR\varphi \colon \mathbb R\rightarrow\mathbb R is a continuous mapping and the set of nonlinearity of φ\varphi has nonzero Lebesgue measure, then φ\varphi maps bijectively a certain set that contains arbitrarily long arithmetic progressions onto a certain set with distinct sums of pairs.

Keywords

Cite

@article{arxiv.1805.02254,
  title  = {Sets with distinct sums of pairs, long arithmetic progressions, and continuous mappings},
  author = {Vladimir Lebedev},
  journal= {arXiv preprint arXiv:1805.02254},
  year   = {2018}
}