论文标题
崩溃的地图和准静态
Collapsing Maps and Quasi-Isometries
论文作者
论文摘要
我们引入了B-Metric的概括，我们称为（B，C）Metric。我们表明，如果$ x $是$（b，c）$ - 公制空间和$ψ：x \ longrightArrow y $是准iS-iSometry，则$ y $ is $ is $（b，c）$ - $ - METRIZABLE。我们还定义了可以应用于任意$（b，c）$ - 公制空间的特定折叠地图。我们在此崩溃的映射的图像上定义了一个距离函数，并证明了崩溃的映射是准静电法。
We introduce a generalization of the b-metric we call a (b,c)-metric. We show that if $X$ is a $(b,c)$-metric space and $ψ: X \longrightarrow Y$ is a quasi-isometry then $Y$ is $(b,c)$-metrizable. We also define a particular kind of collapsing map that can be applied to an arbitrary $(b,c)$-metric space. We define a distance function on the image of this collapsing map and with this prove that the collapsing map is a quasi-isometry.
