Geodesic
Selections of the metric projection operator and strict solarity of sets with continuous metric projection
Sbornik. Mathematics, Tome 208 (2017) no. 7, pp. 915-928

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In a broad class of finite-dimensional Banach spaces, we show that a closed set with lower semicontinuous metric projection is a strict sun, admits a continuous selection of the metric projection operator onto it, has contractible intersections with balls, and its (nonempty) intersection with any closed ball is a retract of this ball. For sets with continuous metric projection, a number of new results relating the solarity of such sets to the stability of the operator of best approximation are obtained. Bibliography 25 titles.
Keywords: sun, strict sun, monotone path-connected set, lower semicontinuous metric projection, selection of the metric projection. 
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     author = {A. R. Alimov},
     title = {Selections of the metric projection operator and strict solarity of sets with continuous metric projection},
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A. R. Alimov. Selections of the metric projection operator and strict solarity of sets with continuous metric projection. Sbornik. Mathematics, Tome 208 (2017) no. 7, pp. 915-928. http://geodesic.mathdoc.fr/item/SM_2017_208_7_a0/