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arXiv · 2505.03767

An affirmative answer to a problem of Cater

Arthur A. Danielyan
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Abstract

Does there exist an increasing absolutely continuous function, $f: [0,1] \rightarrow \mathbb R$ such that $\{x: f'(x)=0\}$ 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.

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Arthur A. Danielyan. 2025-04-25. An affirmative answer to a problem of Cater. https://arxiv.org/abs/2505.03767

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