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arXiv · 2110.11675

Constructing Whitney sets via IFS with condensation

Qi-han Yuan·Yuan Zhang
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Abstract

In 1935, Whitney constructed a smooth function for which the Morse-Sard Theorem does not hold. Whitney's construction is closely related to certain compact connected set, which is called Whitney set now. From then on, there are a lot of works on Whitney sets. In this paper, we use IFS with condensation, a notion introduced by Barnsley and Demko in 1985, to construct Whitney arcs and Whitney sets. Our construction includes most early results as special cases.

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Qi-han Yuan, Yuan Zhang. 2021-10-22. Constructing Whitney sets via IFS with condensation. https://arxiv.org/abs/2110.11675

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