标题： 渐近散射空间 显示英文标题

标题： Asymptotically Scattered Spaces

摘要： 我们将薄的和渐近散射的度量空间分别定义为离散和散射度量空间的渐近对应物。 我们通过禁止的子空间来表征渐近散射的空间，并根据粗等价对薄的度量空间进行分类。 我们引入了渐近散射空间的类型，并构造了不同类型的空间。 我们将渐近散射空间的概念转移到$G$-空间，并表征了群的渐近散射空间。 显示英文摘要

摘要： We define thin and asymptotically scattered metric spaces as asymptotic counterparts of discrete and scattered metric spaces respectively. We characterize asymptotically scattered spaces in terms of prohibited subspaces, and classify thin metric spaces up to coarse equivalence. We introduce the types of asymptotically scattered spaces and construct the spaces of distinct types. We transfer the notion of asymptotically scattered spaces to $G$-spaces and characterize asymptotically scattered spaces of groups.