Geodesic
On finite-dimensional Banach spaces in which suns are connected
Eurasian mathematical journal, Tome 6 (2015) no. 4, pp. 7-18.

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The present paper extends and refines some results on the connectedness of suns in finite-dimensional normed linear spaces. In particular, a sun in a finite-dimensional $(BM)$-space is shown to be monotone path-connected and having a continuous multiplicative (additive) $\varepsilon$-selection from the operator of nearly best approximation for any $\varepsilon>0$. New properties of $(BM)$-space are put forward. 
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A. R. Alimov. On finite-dimensional Banach spaces in which suns are connected. Eurasian mathematical journal, Tome 6 (2015) no. 4, pp. 7-18. http://geodesic.mathdoc.fr/item/EMJ_2015_6_4_a1/

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