A remark about critical sets in $R^3$

Juan Souto (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We give a necessary condition for a closed 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 a critical sets.

Domaines: Topologie géométrique [math.GT]; Analyse classique [math.CA]

Juan Souto. A remark about critical sets in $R^3$. Revista Matemática Iberoamericana, 2019, 35 (2), pp.461-469. ⟨10.4171/RMI/1059⟩. ⟨hal-01389470⟩