Physical Sciences and Mathematics Commons^™

Topology And Infinite Graphs, Nicholas Blackburn Lowery

Honors Papers

The main focus of this paper will be on two very different areas in which topology is relevant to the study of infinite graphs. The first is the mechanics of compactness proofs, which use a particular group of lemmas to extend results about finite subgraphs to apply to an entire infinite graph. We will explore these results by using them to prove a result of de Bruijn and Erdos, that an infinite graph is k-colorable if its finite subgraphs are k-colorable, in several different ways.

The second area is a relatively new area of study pioneered by Diestel which redefines …