Friday, July 20 at 1:30pm

Fields institute, Stewart library

Speaker: David Milovich (Texas A&M)

Title: Davies trees and stratified inverse limits

Abstract: A Davies tree is a method of performing transfinite recursive

constructions longer than $\omega_1$ yet proceeding one countable piece

at a time. At any given stage, the tree organizes all previous stages

into finitely many nice pieces. I will discuss how a simpler structure

induces a canonical Davies tree, extending the applicability of the

Davies tree and simplifying its use. I will also survey some proofs

that use Davies trees. The original such proof (Davies, 1963) shows

(in ZFC) that the plane is a countable union of rotations of graphs of

functions. Most recently, I have used a Davies tree in a proof that

every zero-dimensional openly generated compactum is a continuous

image of a homogeneous zero-dimensional openly generated compactum.