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

arxiv.org. math. Cornell University, 2018. No. arXiv:1805.02254v1.
We show that if a continuous self-mapping of the real line has the set of nonlinearity of nonzero Lebesgue measure, then it maps bijectively a certain set that contains arbitrarily long arithmetic progressions onto a certain set with distinct sums of pairs.