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. 
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/
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