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arXiv · 1108.2625

Continuous Functions that Cut the Real Axis Very Often

Omid Zabeti
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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.

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Omid Zabeti. 2011-08-11. Continuous Functions that Cut the Real Axis Very Often. https://arxiv.org/abs/1108.2625

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