Geodesic
Local solarity of suns in normed linear spaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 3-14.

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The paper is concerned with solarity of intersections of suns with bars (in particular, with closed balls and extreme hyperstrips) in normed linear spaces. A sun in a finite-dimensional $(BM)$-space (in particular, in $\ell^1(n)$) is shown to be monotone path connected. A nonempty intersection of an $\mathrm m$-connected set (in particular, a sun in a two-dimensional space or in a finite-dimensional $(BM)$-space) with a bar is shown to be a monotone path-connected sun. Similar results are obtained for boundedly compact subsets of infinite-dimensional spaces. A nonempty intersection of a monotone path-connected subset of a normed space with a bar is shown to be a monotone path-connected $\alpha$-sun. 
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A. R. Alimov. Local solarity of suns in normed linear spaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 3-14. http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a0/

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