Ernest Schimmerling

Mathematical logic seminar - September 25, 2003

Time: 12 - 1:20 p.m.

Room: CFA 110

Speaker: John Clemens
Assistant Professor
Department of Mathematics
Pennsylvania State University

Title: Distance sets of Polish metric spaces

Abstract: 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.