Constructing Whitney sets via IFS with condensation

作者：Yuan, Qi-han; Zhang, Yuan^*

来源：Journal of Mathematical Analysis and Applications, 2022, 514(1): 126211.

DOI：10.1016/j.jmaa.2022.126211

• Whitney set
• Self-similar arc
• IFS with condensation

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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