Publication at Faculty of Mathematics and Physics |
2022
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 [8]. The paper is however targeted also to specialists in metric geometry and geometry of Banach spaces.