Complexity of distances between metric and Banach spaces

Osoba referująca: 
Michal Doucha (Prague)
Data spotkania seminaryjnego: 
poniedziałek, 19. Luty 2018 - 16:20
We extend the theory of Borel/analytic equivalence relations and reductions between them to the theory of Borel/analytic pseudometrics and reductions between them. This is in the spirit of model theory for metric structures which aims to generalize discrete notions to their continuous counterparts. We consider several classical distances from functional analysis and metric geometry, such as Banach-Mazur distance, Gromov-Hausdorff distance, Kadets distance, Lipschitz distance, etc., and show how they reduce to each other in a Borel way. It is joint work with Marek Cúth and Ondřej Kurka.