Series: Penn State Logic Seminar

Date: Tuesday, October 7, 2003

Time: 2:30 - 3:45 PM

Place: 113 McAllister Building

Speaker: John Clemens, Penn State, Mathematics

Title: Distance Sets of Polish Metric Spaces


A Polish metric space is a separable, complete metric space. 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
real numbers 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.