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

Juan Souto

doi:10.4171/rmi/1059

JournalsrmiVol. 35, No. 2pp. 461–469

A remark about critical sets in $R^{3}$

Juan Souto
Université de Rennes 1, France

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

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Abstract

We give a necessary condition for a subset of $R^{3}$ 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.

Cite this article

Juan Souto, A remark about critical sets in $R^{3}$ . Rev. Mat. Iberoam. 35 (2019), no. 2, pp. 461–469

DOI 10.4171/RMI/1059