THE CLASSICAL TOPOLOGY AND CONE LATTICES

Abstract

In his 2005 dissertation, Antoine Vella introduced a new topology on graphs andhypergraphs known as the "classical" topology. In his 2015 thesis, Brian Fraziercharacterized the prime spectrum for certain graphs' open set lattice under the clas-sical topology and demonstrated how the graph may be recaptured from the primespectrum. In this paper, we further explore the classical topology on simple, socialgraphs by characterizing the classical topology for simple, social graphs order theoret-ically, discussing graph posets and their connection with the classical topology, andcharacterizing the lattices which the classical topology yields, namely cone lattices.