Geodesic
Chebyshev Sets with Piecewise Continuous Metric Projection
Matematičeskie zametki, Tome 113 (2023) no. 6, pp. 905-917

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We study the properties of Chebyshev sets composed of at most countably many sets with a continuous metric projection. Local solarity is established in neighborhoods on which the metric projection is single-valued and continuous in uniformly convex spaces. As examples of applications of the results obtained, we consider generalized fractions and products, as well as ridge functions.
Keywords: uniformly convex spaces, metric projection, Chebyshev sets, local solarity. 
@article{MZM_2023_113_6_a9,
     author = {I. G. Tsar'kov},
     title = {Chebyshev {Sets} with {Piecewise} {Continuous} {Metric} {Projection}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {905--917},
     publisher = {mathdoc},
     volume = {113},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_6_a9/}
}
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I. G. Tsar'kov. Chebyshev Sets with Piecewise Continuous Metric Projection. Matematičeskie zametki, Tome 113 (2023) no. 6, pp. 905-917. http://geodesic.mathdoc.fr/item/MZM_2023_113_6_a9/