论文标题
地球空间的边界
Boundaries for geodesic spaces
论文作者
论文摘要
For every proper geodesic space $X$ we introduce its quasi-geometric boundary $\partial_{QG}X$ with the following properties: 1. Every geodesic ray $g$ in $X$ converges to a point of the boundary $\partial_{QG}X$ and for every point $p$ in $\partial_{QG}X$ there is a geodesic ray in $X$ converging to $ p $，2。边界$ \ partial_ {qg} x $是紧凑的公制，3。边界$ \ partial_ {qg} x $是一个不变的，在准等级等价下，4。quasi ismotemmotem嵌入式嵌入Quasi-Geodesic bundaries的连续映射，然后If $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x grom。 $ \ partial_ {qg} x $是$ x $的gromov边界。 6。如果$ x $是一个croke-kleiner空间，则$ \ partial_ {qg} x $是一个点。
For every proper geodesic space $X$ we introduce its quasi-geometric boundary $\partial_{QG}X$ with the following properties: 1. Every geodesic ray $g$ in $X$ converges to a point of the boundary $\partial_{QG}X$ and for every point $p$ in $\partial_{QG}X$ there is a geodesic ray in $X$ converging to $p$, 2. The boundary $\partial_{QG}X$ is compact metric, 3. The boundary $\partial_{QG}X$ is an invariant under quasi-isometric equivalences, 4. A quasi-isometric embedding induces a continuous map of quasi-geodesic boundaries, 5. If $X$ is Gromov hyperbolic, then $\partial_{QG}X$ is the Gromov boundary of $X$. 6. If $X$ is a Croke-Kleiner space, then $\partial_{QG}X$ is a point.
