Geodesic
Locally Chebyshev Sets on the Plane
Matematičeskie zametki, Tome 97 (2015) no. 1, pp. 142-149

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The notion of locally Chebyshev set is introduced and the relationship between Chebyshev and locally Chebyshev sets on the plane is studied. It is shown that any connected closed locally Chebyshev set in an arbitrary Banach space is a Chebyshev set and each Chebyshev set is locally Chebyshev if and only if the space is strictly convex.
Keywords: Chebyshev set, locally Chebyshev set, metric projection, Banach space. 
@article{MZM_2015_97_1_a13,
     author = {A. A. Flerov},
     title = {Locally {Chebyshev} {Sets} on the {Plane}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {142--149},
     publisher = {mathdoc},
     volume = {97},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_1_a13/}
}
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A. A. Flerov. Locally Chebyshev Sets on the Plane. Matematičeskie zametki, Tome 97 (2015) no. 1, pp. 142-149. http://geodesic.mathdoc.fr/item/MZM_2015_97_1_a13/