论文标题
量子异构体和松散的嵌入
Quantum isometries and loose embeddings
论文作者
论文摘要
我们表明，可数的度量空间始终具有量子标准组，从而扩展了已知具有这种通用量子组作用的度量空间。 由这个存在问题的激励，我们定义和研究了公制空间$（x，d_x）$松散的嵌入性的概念，$（y，d_y）$：存在一个具有距离的注射式连续地图，该地图既可以保留距离的平等和不等式。我们表明，即使并非所有可计数的度量空间都是，$ 0 $维度紧凑的度量空间都可以“一般”松散地嵌入实际线路。
We show that countable metric spaces always have quantum isometry groups, thus extending the class of metric spaces known to possess such universal quantum-group actions. Motivated by this existence problem we define and study the notion of loose embeddability of a metric space $(X,d_X)$ into another, $(Y,d_Y)$: the existence of an injective continuous map that preserves both equalities and inequalities of distances. We show that $0$-dimensional compact metric spaces are "generically" loosely embeddable into the real line, even though not even all countable metric spaces are.
