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- ДокументOn semiconvexity of open sets with smooth boundary in the plane(2020) Tetiana OsipchukThe present work considers properties of classes of generally convex sets in the plane known as 1-semiconvex and weakly 1-semiconvex. More specifically, it is proved that open, weakly 1-semiconvex but not 1-semiconvex set with smooth boundary in the plane consists of not less than four connected components.