Descriptive Set Theory and Measure Theory in Locally Compact and Non-locally Compact Groups
Description:
In this thesis we study descriptive-set-theoretic and measure-theoretic properties of Polish groups, with a thematic emphasis on the contrast between groups which are locally compact and those which are not. The work is divided into three major sections. In the first, working jointly with Robert Kallman, we resolve a conjecture of Gleason regarding the Polish topologization of abstract groups of homeomorphisms. We show that Gleason's conjecture is false, and its conclusion is only true when the…
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Date:
May 2013
Creator:
Cohen, Michael Patrick
Partner:
UNT Libraries