|Time:|| 12 - 1:20 p.m.
Department of Mathematics
Pennsylvania State University
Distance sets of Polish metric spaces
A Polish metric space is a Polish space equipped with a complete,
compatible metric. The distance set of the metric space is the set of all
distances between pairs of points in the space. I will first characterize
which sets of reals can be the set of distances of some Polish metric
space. I will then consider how close the distance set is to being a
complete invariant for isometry of Polish metric spaces, and discuss how
the theory of definable equivalence relations can be used to show that, in
general, it is very far from being a complete invariant.
|Organizer's note:|| This week, lunch will be provided.