论文标题
lorentzian长度空间的Gromov-Hausdorff指标和尺寸
Gromov-Hausdorff metrics and dimensions of Lorentzian length spaces
论文作者
论文摘要
我们为洛伦兹距离构造了Gromov-Hausdorff空间的类似物，并为其中一个显示了Gromov的预熟度。 After calculating the Dushnik-Miller dimension of Minkowski spaces (of manifold dimension larger than 2) to be countable infinity, we define a dimension for ordered sets recovering the correct manifold dimension, obtain an obstruction for existence of injective monotonous maps between Lorentzian length spaces, induce functorial pseudo-metrics on Cauchy subsets that in the spacetime case coincide with the riemannian且证明具有给定的cauchy零基因座的抗Lipschitz cauchy函数是Sormani-Vega无效距离的基本要素。
We construct analoga of Gromov-Hausdorff space for Lorentzian distances and show a Gromov precompactness result for one of them. After calculating the Dushnik-Miller dimension of Minkowski spaces (of manifold dimension larger than 2) to be countable infinity, we define a dimension for ordered sets recovering the correct manifold dimension, obtain an obstruction for existence of injective monotonous maps between Lorentzian length spaces, induce functorial pseudo-metrics on Cauchy subsets that in the spacetime case coincide with the Riemannian ones, and prove existence of anti-Lipschitz Cauchy functions with a given Cauchy zero locus, a fundamental ingredient for the Sormani-Vega null distance.
