COMPLEXITY OF DISTANCES: REDUCTIONS OF DISTANCES BETWEEN METRIC AND BANACH SPACES

Abstrakt

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.

Klíčová slova

• COMPLEXITY
• REDUCTIONS
• DISTANCES
• BANACH SPACES