JEWLScholar@MTSU Repository

A Duality between hypergraphs and cone lattices

Show simple item record

dc.contributor.advisor Hart, James French, Zack 2018-06-05T20:04:52Z 2018-06-05T20:04:52Z 2018-03-22
dc.description.abstract In this paper, we introduce and characterize the class of lattices that arise as the
dc.description.abstract family of lowersets of the incidence poset for a hypergraph. In particular, we show
dc.description.abstract that the following statements are logically equivalent:
dc.description.abstract 1. A lattice L is order isomorphic to the frame of opens for a hypergraph endowed
dc.description.abstract with the Classical topology.
dc.description.abstract 2. A lattice L is bialgebraic, distributive, and its subposet of completely joinprime
dc.description.abstract elements forms the incidence poset for a hypergraph.
dc.description.abstract 3. A lattice L is a cone lattice.
dc.description.abstract We conclude the paper by extending a well-known Stone-type duality to the categories
dc.description.abstract of hypergraphs coupled with finite-based HP-morphisms and cone lattices
dc.description.abstract coupled with frame homomorphisms that preserve compact elements.
dc.publisher Middle Tennessee State University
dc.title A Duality between hypergraphs and cone lattices
dc.type Thesis
dc.contributor.committeemember Sarkar, Medha
dc.contributor.committeemember Ye, Dong
dc.thesis.degreelevel Masters
dc.thesis.degreegrantor Middle Tennessee State University
dc.subject.umi Mathematics M.S.
dc.contributor.department College of Basic & Applied Sciences

Files in this item

This item appears in the following Collection(s)

Show simple item record

Search JEWLScholar@MTSU


My Account