Topology Seminar

SPEAKER: Mr. Kyle Austin

TITLE: Partitions of Unity - 3

ABSTRACT: The purpose of this presentation is to introduce partitions of unity and their applications to topology and analysis. This should give an interesting new point of view for normal and paracompact spaces. The presentation will follow the paper "Partitions of Unity" by Jerzy Dydak. In particular, we will use partitions of unity to prove variants of Teitze Extension Theorem which in turn will be used to prove some classical results about normal and paracompact spaces. The notion of equicontinuous partitions of arbitrary functions will be introduced. We will use this idea to create certain partitions of unity with nice properties and to give a useful characterization of when a normal space is paracompact.