Geodesic
Preservation of approximative properties of subsets
Izvestiya. Mathematics , Tome 70 (2006) no. 5, pp. 857-866

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We describe the subsets $\Pi\subset\mathbb R^n$ whose intersection with a Chebyshev set (sun, or strict sun) $M$ in $\ell^\infty(n)$ preserves the approximative properties of $M$ in $\ell^\infty(n)$. 
@article{IM2_2006_70_5_a0,
     author = {A. R. Alimov},
     title = {Preservation of approximative properties of subsets},
     journal = {Izvestiya. Mathematics },
     pages = {857--866},
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     volume = {70},
     number = {5},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_5_a0/}
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A. R. Alimov. Preservation of approximative properties of subsets. Izvestiya. Mathematics , Tome 70 (2006) no. 5, pp. 857-866. http://geodesic.mathdoc.fr/item/IM2_2006_70_5_a0/