Geodesic
On compactness and connectedness of the paratingent
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 70 (2016) no. 2 
Zygmunt, Wojciech. On compactness and connectedness of the paratingent. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 70 (2016) no. 2. http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a5/
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Voir la notice de l'article provenant de la source Library of Science

In this note we shall prove that for a continuous function φ : Δ→ℝ^n, where Δ⊂ℝ,  the paratingent of φ at a∈Δ is a non-empty and compact set in ℝ^n if and only if φ satisfies Lipschitz condition in a neighbourhood of a. Moreover, in this case the paratingent is a connected set.

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