Geodesic
A Decomposition Theorem for m-Convex Sets in Rd
Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 1051-1057

Voir la notice de l'article provenant de la source Cambridge University Press

Let S be a subset of some linear topological space. The set S is said to be m-convex, m ≧ 2, if and only if for every m-member subset of S, at least one of the line segments determined by these points lies in S. A point x in S is said to be a point of local convexity of S if and only if there is some neighborhood N of x such that if y, z Є N ⌒ S, then [y, z] ⊆ S. If S fails to be locally convex at some point a in S, then q is called a point of local nonconvexity (lnc point) of S. 
Breen, Marilyn. A Decomposition Theorem for m-Convex Sets in Rd. Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 1051-1057. doi: 10.4153/CJM-1976-102-5
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