English

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}
}
R2 v1 2026-06-24T07:06:01.590Z