A Duality between hypergraphs and cone lattices

French, Zack

dc.contributor.advisor	Hart, James
dc.contributor.author	French, Zack
dc.date.accessioned	2018-06-05T20:04:52Z
dc.date.available	2018-06-05T20:04:52Z
dc.date.issued	2018-03-22
dc.identifier.uri	http://jewlscholar.mtsu.edu/xmlui/handle/mtsu/5660
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
dc.description.degree	M.S.
dc.contributor.department	College of Basic & Applied Sciences