Geodesic
Star-shapedness and co-star-shapedness of finite unions and intersections of closed half-spaces
Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 134-147

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In the paper we answer the question when in finite dimensions finite unions and intersections of closed half-spaces are shifts of sets stable under shrinkings or dilatations and give explicit descriptions of the kernels of such sets. 
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     title = {Star-shapedness and co-star-shapedness of finite unions and intersections of closed half-spaces},
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A. P. Shveidel. Star-shapedness and co-star-shapedness of finite unions and intersections of closed half-spaces. Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 134-147. http://geodesic.mathdoc.fr/item/EMJ_2010_1_3_a7/