Revista Matemática Iberoamericana

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Volume 35, Issue 2, 2019, pp. 461–469
DOI: 10.4171/rmi/1059

Published online: 2019-04-15

A remark about critical sets in $\mathbb R^3$

Juan Souto[1]

(1) Université de Rennes 1, France

We give a necessary condition for a subset of $\mathbb R^3$ 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 critical sets.

Keywords: Critical sets, Whitehead manifold, tameness

Souto Juan: A remark about critical sets in $\mathbb R^3$. Rev. Mat. Iberoam. 35 (2019), 461-469. doi: 10.4171/rmi/1059