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arXiv · 2004.11752

Complexity of distances: Reductions of distances between metric and Banach spaces

Marek Cúth·Michal Doucha·Ondřej Kurka
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Abstract

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.

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Marek Cúth, Michal Doucha, Ondřej Kurka. 2021-01-26. Complexity of distances: Reductions of distances between metric and Banach spaces. https://doi.org/10.1007/s11856-022-2305-7

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