English

Continuous Functions that Cut the Real Axis Very Often

Classical Analysis and ODEs 2015-03-19 v3

Abstract

We consider continuous functions f : [0,1] \to R that cut the real axis at every point of a measurable set of positive measure and we construct examples where f fails to have bounded variation, and at the opposite end, where f admits derivatives of all orders.

Keywords

Cite

@article{arxiv.1108.2625,
  title  = {Continuous Functions that Cut the Real Axis Very Often},
  author = {Omid Zabeti},
  journal= {arXiv preprint arXiv:1108.2625},
  year   = {2015}
}

Comments

4 pages

R2 v1 2026-06-21T18:49:46.930Z