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Abstract
The present work considers properties of generally convex sets in real three-dimensional space R3 known as weakly 2-convex. An open set in R3 is called weakly 2-convex if through every boundary point of the set there passes a plane not intersecting the given set. A closed set in R3 is called weakly 2-convex if it is approximated from the outside by a family of open weakly 2-convex sets. A point of the complement of a set in R3 to the whole space is a 2-nonconvexity point of the set if every plane passing through the point intersects the set. It is proved that the non-empty interior of a closed weakly 2-convex set is weakly 2-convex. It is shown that for any convex polyhedron there exists an open weakly 2-convex set such that its 2-nonconvexity-point set coincides with the polyhedron interior, but there exists an open weakly 2-convex set such that its open bounded convex 2-nonconvexity-point set differs from the interior of a convex polyhedron.
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