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Regular version of the site

Working paper

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

arxiv.org. math. Cornell University, 2018. No. arXiv:1805.02254v2.
We show that if ϕ: R → R is a continuous mapping and the set of nonlinearity of ϕ has nonzero Lebesgue measure, then ϕ maps bijectively a certain set that contains arbitrarily long arithmetic progressions onto a certain set with distinct sums of pairs.