Geodesic
Approximative and structural properties of sets in asymmetric spaces
Izvestiya. Mathematics , Tome 86 (2022) no. 6, pp. 1240-1253

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Structural and approximative properties of sets implying their solarity are studied. It is shown that, in any finite-dimensional polyhedral space, each strict sun admits a continuous $\varepsilon$-selection for all $\varepsilon>0$ and the metric projection onto it has cell-like values. In general asymmetric spaces, sufficient conditions for solarity of Chebyshev sets are put forward.
Keywords: cell-like set, sun, asymmetric space, polyhedral space, Chebyshev set. 
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     author = {I. G. Tsar'kov},
     title = {Approximative and structural properties of sets in asymmetric spaces},
     journal = {Izvestiya. Mathematics },
     pages = {1240--1253},
     publisher = {mathdoc},
     volume = {86},
     number = {6},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2022_86_6_a10/}
}
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I. G. Tsar'kov. Approximative and structural properties of sets in asymmetric spaces. Izvestiya. Mathematics , Tome 86 (2022) no. 6, pp. 1240-1253. http://geodesic.mathdoc.fr/item/IM2_2022_86_6_a10/