论文标题
尖头的Gromov-Hausdorff拓扑稳定性，用于非紧凑型公制空间
Pointed Gromov-Hausdorff Topological Stability for non-compact metric spaces
论文作者
论文摘要
我们将尖头的Gromov-Hausdorff公制[RON10]与本地$ C^0 $距离相结合，以获得尖头的$ C^0 $ -Gromov-Hausdorff距离之间可能不同的非紧凑型指标空间之间的地图之间的距离。然后将后者与Walters的本地拓扑稳定性[LNY18]和[AMR17]的$ gh $稳定性结合在一起，以获取拓扑上$ GH $稳定的同质形态的概念。我们举一个例子以显示距离指标空间中不同基点时距离之间的差异。
We combine the pointed Gromov-Hausdorff metric [Ron10] with the locally $C^0$ distance to obtain the pointed $C^0$-Gromov-Hausdorff distance between maps of possibly different non-compact pointed metric spaces. The latter is then combined with Walters's locally topological stability [LNY18] and $GH$-stability from [AMR17] to obtain the notion of topologically $GH$-stable pointed homeomorphism. We give one example to show the difference between the distance when take different base point in a pointed metric space.
