论文标题
通过传输边界函子保存的某些属性
Some properties that are preserved by transferring boundary functors
论文作者
论文摘要
如果Hausdorff局部紧凑的副干燥空间具有粗糙的结构，则有一个与之相关的良好的紧凑型家族。如果有两个空间，即$ x $和$ y $，具有良好的粗略等价，那么这些紧凑型的$ x $和$ y $的家族之间存在信件。另一方面，如果一个$ g $在Hausdorff本地空间$ x $上具有正确的不连续的CoCompact动作，则在$ G $的尼斯紧凑型与$ x $的尼斯紧凑型之间也有一个对应关系。在本文中，我们表明，当涉及概念（粗糙的结构和群体作用）时，紧凑型家族的两个对应关系一致。我们还证明，这些对应关系必须保留压缩的一些几何特性。
If a Hausdorff locally compact paracompact space has a coarse structure, then there is a family of well behaved compactifications associated to it. If there are two of these spaces, $X$ and $Y$, with a good coarse equivalence, then there is a correspondence between these families of compactifications of $X$ and $Y$. On the other hand, if a group $G$ has a properly discontinuous cocompact action on a Hausdorff locally space $X$, then there is also a correspondence between nice compactifications of $G$ and nice compactifications of $X$. In this paper we show that when there are both concepts involved (coarse structure and group action), then both correspondences of families of compactifications agree. We also prove that these correspondences must preserve some geometric properties of the compactifications.
