Geodesic
On compactness and connectedness of the paratingent
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 70 (2016) no. 2.

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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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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/

[1] Aubin, J. P., Frankowska, H., Set-Valued Analysis, Birkhauser, Boston, Massachusetts, 1990.

[2] Bielecki, A., Sur certaines conditions necessaires et suffisantes pour l’unicite des solutions des systemes d’equations differentielles ordinaires et des equations au paratingent, Ann. Univ. Mariae Curie-Skłodowska Sect. A 2 (1948), 49-106.

[3] Bouligand, G., Introduction a la geometrie infinitesimale directe, Vuibert, Paris, 1932.

[4] Choquet, G., Outils topologiques et metriques de l’analyse mathematique, Centre de Documentation Univ., Course redige par C. Mayer, Paris, 1969.

[5] Fedor, M., Szyszkowska, J., Darboux properties of the paratingent, Ann. Univ. Mariae Curie-Skłodowska Sect. A 62 (2008), 67-74.

[6] Mirica, S., The contingent and the paratingent as generalized derivatives for vectorvalued and set-valued mappings, Nonlinear Anal. 6 (1982), 1335-1368.