On strict suns in $\ell^\infty(3)$

Abstract

A subset M of a normed linear space X is said to be a {\it strict sun} if, for every point $x\in X\setminus M$, the set of its nearest points from~$M$ is non-empty and if $y\in M$ is a nearest point from M to x, then y is a nearest point from M to all points from the ray $\{λx+(1- λ)y | λ>0\}$. In the paper there obtained a geometrical characterisation of strict suns in $\ell^\infty(3)$.