Geodesic
Sets with not more than two-valued metric projection on planes
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 14-19 
A. A. Flerov. Sets with not more than two-valued metric projection on planes. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2013), pp. 14-19. http://geodesic.mathdoc.fr/item/VMUMM_2013_6_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a set $M$ in the Euclidean plane $\mathbb{R}^2$, we prove that if any point $x\in\mathbb{R}^2$ has one or two closest points in $M$, then each point of the convex hull of $M$ lies in the segment with endpoints in $M$.

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