论文标题
距离的复杂性：公制空间和Banach空间之间距离的降低
Complexity of distances: Reductions of distances between metric and Banach spaces
论文作者
论文摘要
我们表明，与公制几何和功能分析的所有标准距离，例如Gromov-Hausdorff距离，Banach-Mazur距离，Kadets距离，Lipschitz距离，净距离和Hausdorff-lipschitz距离都具有相同的复杂性，并且可以在精确定义的方式中彼此降低。 这是根据描述性集理论来完成的，是作者在\ emph {距离的复杂性：广义分析等效关系理论}中发起的较大研究计划的一部分。但是，该论文也针对Banach空间的公制几何形状和几何形状的专家。
We show that all the standard distances from metric geometry and functional analysis, such as Gromov-Hausdorff distance, Banach-Mazur distance, Kadets distance, Lipschitz distance, Net distance, and Hausdorff-Lipschitz distance have all the same complexity and are reducible to each other in a precisely defined way. This is done in terms of descriptive set theory and is a part of a larger research program initiated by the authors in \emph{Complexity of distances: Theory of generalized analytic equivalence relations}. The paper is however targeted also to specialists in metric geometry and geometry of Banach spaces.
