论文标题
关于在有限维规范空间中具有凸紧comvex的一个操作的连续性
About the continuity of one operation with convex compacts in finite-dimensional normed spaces
论文作者
论文摘要
在本文中，我们研究了一个紧凑型套件与另一个紧凑型的封闭邻居的交点的变形，这是通过改变该邻域的半径的。结果表明，在有限维定的规范空间中，在两个紧凑型集合都是非空的凸子集的情况下，这种操作是由Hausdorff Metric产生的拓扑连续的。所描述的交集对邻居半径的连续依赖性的问题是极端网络理论发展的副产品。但是，事实证明它本身很有趣，这表明了各种概括。因此，决定单独发布。
In this paper, we study the deformation of the intersection of one compact set with a closed neighborhood of another compact set by changing the radius of this neighborhood. It is shown that in finite-dimensional normed spaces, in the case when both compact sets are non-empty convex subsets, such an operation is continuous in the topology generated by the Hausdorff metric. The question of the continuous dependence of the described intersection on the radius of the neighborhood arose as a by-product of the development of the theory of extremal networks. However, it turned out to be interesting in itself, suggesting various generalizations. Therefore, it was decided to publish it separately.
