Geodesic
Characterization of Sets with Continuous Metric Projection in the Space~$\ell^\infty_n$
Matematičeskie zametki, Tome 108 (2020) no. 3, pp. 323-333.

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We characterize the subsets of the space $\ell^\infty_n$ with continuous (lower semicontinuous) metric projection. One of the characteristic properties is the strict solarity of both the set and any nonempty intersection thereof with any support coordinate hyperplane.
Keywords: strict sun, continuity of metric projection, lower semicontinuity of metric projection, strictly monotone path-connected set. 
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A. R. Alimov. Characterization of Sets with Continuous Metric Projection in the Space~$\ell^\infty_n$. Matematičeskie zametki, Tome 108 (2020) no. 3, pp. 323-333. http://geodesic.mathdoc.fr/item/MZM_2020_108_3_a0/

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