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. 
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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/

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