Abstract We investigate properties which remain invariant under the action of quasi-Möbius maps of quasimetric spaces. A metric space is called doubling with constant D if every ball of finite radius can be covered by at most D balls of half the radius. It is shown that the doubling property is an invariant property for (quasi-)Möbius maps. Additionally it is shown that the property of uniform disconnectedness is an invariant for (quasi-)Möbius maps as well.

中文翻译：

---

拟莫比乌斯图的一些不变性质

摘要 我们研究在拟度量空间的拟莫比乌斯图作用下保持不变的性质。如果每个有限半径的球最多可以被半径一半的 D 个球覆盖，则度量空间称为具有常数 D 的倍增。结果表明，倍增性质是（拟）莫比乌斯图的不变性质。此外还表明，均匀断开的特性也是（准）莫比乌斯图的不变量。