THE CLASSICAL TOPOLOGY AND CONE LATTICES

Abstract

In his 2005 dissertation, Antoine Vella introduced a new topology on graphs and

hypergraphs known as the "classical" topology. In his 2015 thesis, Brian Frazier

characterized the prime spectrum for certain graphs' open set lattice under the clas-

sical topology and demonstrated how the graph may be recaptured from the prime

spectrum. In this paper, we further explore the classical topology on simple, social

graphs by characterizing the classical topology for simple, social graphs order theoret-

ically, discussing graph posets and their connection with the classical topology, and

characterizing the lattices which the classical topology yields, namely cone lattices.