Geodesic
Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets
Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 483-493.

Voir la notice de l'article provenant de la source Math-Net.Ru

In a two-dimensional Banach space $X$, the class of Chebyshev sets coincides with the class of closed and monotone path-connected sets if and only if $X$ is strictly convex. In a finite-dimensional Banach space $X$ of dimension at least $3$, this coincidence occurs if and only if $X$ is smooth and strictly convex.
Keywords: Chebyshev set, convexity, monotone path-connectedness, smoothness. 
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B. B. Bednov. Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets. Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 483-493. http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a0/

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