DMS Topology Seminar

Speakers: Michel Smith and Haley Pavlis 

(Haley Pavlis)

Abstract: We define the graph topology for finite graphs. We discuss the properties of a continuous map between graphs and properties of a traditional inverse limit of graphs. Most importantly, that a traditional inverse limit of finite path graphs is non-Hausdorff. We introduce a generalized inverse limit, where the first space is a metric arc and all other spaces are finite path graphs. Using the Bucket Handle continuum as an example, a technique is shown for constructing a generalized inverse limit, where the first space is a metric arc and the others are finite path graphs, that is homeomorphic to a traditional inverse limit of Hausdorff arcs.

Using crooked chains, we construct and analyze a non-Hausdorff hereditarily indecomposable continuum. This continuum has some interesting properties, which will be discussed. Ongoing research is discussed and open problems stated.

(Michel Smith)

Title: Non-metric Hereditarily Indecomposable Continua.

Abstract: We discuss techniques for producing non-metric hereditarily indecomposable continua. Examples are presented.  However, attempts to generalize metric construction techniques yield situations in which hereditary indecomposability implies metrizability. We review our recent results regarding such situations.  Open problems in the area are stated.