Kurt Gödel Research Center

2013 seminar talk: Strong measure zero in metric spaces and Polish groups

Talk held by Michael Hrušák (Universidad Nacional Autónoma de México) at the KGRC seminar on 2013-12-19.

Abstract

We shall study the notion of strong measure zero in a general setting of a separable metric space. We shall investigate to what extent can the theorem of Galvin, Mycielski and Solovay be extended to an arbitrary Polish group. We shall also see that there are two classes of separable metric spaces on which the notion of strong measure zero behaves differently. The dividing line being provided by the so called small ball property.

This is joint work with W. Wohofsky and O. Zindulka.