Constructing Whitney sets via IFS with condensation
Metric Geometry
2021-10-25 v1
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.
Cite
@article{arxiv.2110.11675,
title = {Constructing Whitney sets via IFS with condensation},
author = {Qi-han Yuan and Yuan Zhang},
journal= {arXiv preprint arXiv:2110.11675},
year = {2021}
}