论文标题
在飞机上的半号套装上
On semiconvex sets in the plane
论文作者
论文摘要
目前的工作考虑了该飞机中通常凸的类别的属性，称为$ 1 $ - sypoomonvex和弱$ 1 $ - sypemiconvex。更具体地说，构建了空地和封闭的弱$ 1 $ sypoomenvex的例子，但在飞机中构建了平滑边界的非$ 1 $ - s型套件。事实证明，此类集合由至少四个连接的组件组成。此外，构建了由三个连接组件组成的封闭，弱$ 1 $ sypoomenvex和非$ 1 $ sypoomonvex设置的示例。事实证明，对于任何封闭的，弱的$ 1 $ sypemiconvex和非$ 1 $ sypemicOnvex设置的封闭，$ 1 $ sypemonvex是最小的。
The present work considers the properties of classes of generally convex sets in the plane known as $1$-semiconvex and weakly $1$-semiconvex. More specifically, the examples of open and closed weakly $1$-semiconvex but non $1$-semiconvex sets with smooth boundary in the plane are constructed. It is proved that such sets consist of minimum four connected components. In addition, the example of closed, weakly $1$-semiconvex, and non $1$-semiconvex set in the plane consisting of three connected components is constructed. It is proved that such a number of components is minimal for any closed, weakly $1$-semiconvex, and non $1$-semiconvex set in the plane.
