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. 
@article{MZM_2022_111_4_a0,
     author = {B. B. Bednov},
     title = {Finite-Dimensional {Spaces} where the {Class} of {Chebyshev} {Sets} {Coincides} with the {Class} of {Closed} and {Monotone} {Path-Connected} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--493},
     publisher = {mathdoc},
     volume = {111},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a0/}
}
TY  - JOUR
AU  - B. B. Bednov
TI  - Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets
JO  - Matematičeskie zametki
PY  - 2022
SP  - 483
EP  - 493
VL  - 111
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a0/
LA  - ru
ID  - MZM_2022_111_4_a0
ER  - 
%0 Journal Article
%A B. B. Bednov
%T Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets
%J Matematičeskie zametki
%D 2022
%P 483-493
%V 111
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a0/
%G ru
%F MZM_2022_111_4_a0
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/