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. 
@article{MZM_2020_108_3_a0,
     author = {A. R. Alimov},
     title = {Characterization of {Sets} with {Continuous} {Metric} {Projection} in the {Space~}$\ell^\infty_n$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--333},
     publisher = {mathdoc},
     volume = {108},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_3_a0/}
}
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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/