English

A remark about critical sets in $R^3$

Geometric Topology 2016-10-07 v1 Classical Analysis and ODEs

Abstract

We give a necessary condition for a closed subset of R3R^3 to be the set of critical points of some smooth function. In particular we obtain that for example neither the Whitehead continuum nor the p-adic solenoid are such a critical sets.

Cite

@article{arxiv.1610.01979,
  title  = {A remark about critical sets in $R^3$},
  author = {Juan Souto},
  journal= {arXiv preprint arXiv:1610.01979},
  year   = {2016}
}

Comments

9 pages

R2 v1 2026-06-22T16:13:26.126Z