Geodesic
Points of Local Nonconvexity and Finite Unions of Convex Sets
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 376-383

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

Let 5 be a subset of Rd. A point x in 5 is a point of local convexity of S if and only if there is some neighborhood U of x such that, if y, z ε 5 ⌒ U, then [y, z] ⊆ S. If S fails to be locally convex at some point q in 5, then q is called a point of local nonconvexity (lnc point) of S.Several interesting properties are known about sets whose lnc points Q may be decomposed into n convex sets. For S closed, connected, S ∼ Q connected, and Q having cardinality n, Guay and Kay [2] have proved that S is expressible as a union of n + 1 or fewer closed convex sets (and their result is valid in a locally convex topological vector space). 
Breen, Marilyn. Points of Local Nonconvexity and Finite Unions of Convex Sets. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 376-383. doi: 10.4153/CJM-1975-046-6
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