# David Milovich: Davies trees and stratified inverse limits

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.