Wednesday, September 02, 2020
12:00 PM -
1:00 PM
Online Event
Logic Seminar
Series: Logic Seminar Series
A dichotomy for Polish modules
Joshua Frisch,
Department of Mathematics,
Caltech,
A Polish module is a topological module whose underlying topology is Polish. In this talk, I will discuss some very recent work (joint with Forte Shinko) where we study when uncountable Polish modules continuously inject into one another and the pre-order induced by these injections. In particular we will show that, for a wide class of rings, there are countably many minimal elements in this pre-order. As an application, we will construct a countable family of uncountable abelian Polish groups, at least one of which embeds into any other uncountable abelian Polish group.
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