Geodesic
Several theorems of combinatorial geometry
Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 117-124.

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A set is said to be $H$-convex if it can be represented by an intersection of a family of closed half-spaces whose outer normals belong to a given subset of the set $H$ of the unit sphere $S^{n-1}\subset R$. On the basis of Helly's theorem for $H$-convex sets recently obtained by us, we prove in this note certain extensions of Blaschke's theorem (on the radius of an inscribed sphere) and of several other well-known theorems of combinatorial geometry. 
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     author = {V. G. Boltyanskii},
     title = {Several theorems of combinatorial geometry},
     journal = {Matemati\v{c}eskie zametki},
     pages = {117--124},
     publisher = {mathdoc},
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     number = {1},
     year = {1977},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a13/}
}
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V. G. Boltyanskii. Several theorems of combinatorial geometry. Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 117-124. http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a13/