Geodesic
Geometrical Characterization of Strict Suns in $\ell^\infty(n)$
Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 3-11.

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A subset $M$ of a normed linear space $X$ is called a strict sun if, for any $x\in X\setminus M$, the set of its nearest points from $M$ is nonempty and for any point $y\in M$ which is nearest to $x$, the point $y$ is a nearest point from $M$ to any point of the ray $\{\lambda x+(1-\lambda)y\mid\lambda>0\}$. We give an intrinsic geometrical characterization of strict suns in the space $\ell^\infty(n)$. 
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A. R. Alimov. Geometrical Characterization of Strict Suns in $\ell^\infty(n)$. Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/MZM_2001_70_1_a0/

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