English

An affirmative answer to a problem of Cater

General Mathematics 2025-05-08 v1

Abstract

Does there exist an increasing absolutely continuous function, f:[0,1]Rf: [0,1] \rightarrow \mathbb R such that {x:f(x)=0}\{x: f'(x)=0\} is both countable and dense? This problem was proposed by F.S. Cater about two decades ago. We give an affirmative answer to the problem.

Cite

@article{arxiv.2505.03767,
  title  = {An affirmative answer to a problem of Cater},
  author = {Arthur A. Danielyan},
  journal= {arXiv preprint arXiv:2505.03767},
  year   = {2025}
}
R2 v1 2026-06-28T23:23:23.362Z