On weakly 1-convex sets in the plane
| dc.contributor.author | Тетяна Осіпчук, Максим Володимирович Ткачук | |
| dc.date.accessioned | 2023-05-10T13:23:46Z | |
| dc.date.available | 2023-05-10T13:23:46Z | |
| dc.date.issued | 2023 | |
| dc.description.abstract | The present work considers the properties of generally convex sets in the plane known as weakly 1-convex. An open set is called weakly 1-convex if for any boundary point of the set there exists a straight line passing through this point and not intersecting the given set. A closed set is called weakly 1-convex if it is approximated from the outside by a family of open weakly 1-convex sets. A point of the complement of a set to the whole plane is called a 1-nonconvexity point of the set if any straight passing through the point intersects the set. It is proved that if an open, weakly 1-convex set has a non-empty set of 1-nonconvexity points, then the latter set is also open. It is also shown that the non-empty interior of a closed, weakly 1-convex set in the plane is weakly 1-convex. | |
| dc.identifier.issn | 2409-8906 | |
| dc.identifier.uri | https://card-file.ontu.edu.ua/handle/123456789/25013 | |
| dc.source | Proceedings of the International Geometry Center | |
| dc.title | On weakly 1-convex sets in the plane |