On weakly m-convex sets

1Dakhil, HK, 2Zelinskii, Yu.B, 2Klishchuk, BA
1Taras Shevchenko National University of Kyiv
2Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2017, 4:3-6
Section: Mathematics
Language: Ukrainian
Some properties of weakly m-convex sets are studied. Various variants of the problem of shadow are investigated. The lower bound for the number of balls that are necessary to create a shadow at a point tangential to sphere $S^{2}$ in the Euclidean space $\mathbb{R}^{3}$, is obtained.
Keywords: 1-hull of a family of sets, conjugate set, Grassmann manifold, m-convex set, problem of shadow, weakly m-convex set
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