A Duality between hypergraphs and cone lattices

Simple item page
dc.contributor.advisorHart, James
dc.contributor.authorFrench, Zack
dc.contributor.committeememberSarkar, Medha
dc.contributor.committeememberYe, Dong
dc.contributor.departmentBasic & Applied Sciencesen_US
dc.date.accessioned2018-06-05T20:04:52Z
dc.date.available2018-06-05T20:04:52Z
dc.date.issued2018-03-22
dc.description.abstractIn this paper, we introduce and characterize the class of lattices that arise as the
dc.description.abstractfamily of lowersets of the incidence poset for a hypergraph. In particular, we show
dc.description.abstractthat the following statements are logically equivalent:
dc.description.abstract1. A lattice L is order isomorphic to the frame of opens for a hypergraph endowed
dc.description.abstractwith the Classical topology.
dc.description.abstract2. A lattice L is bialgebraic, distributive, and its subposet of completely joinprime
dc.description.abstractelements forms the incidence poset for a hypergraph.
dc.description.abstract3. A lattice L is a cone lattice.
dc.description.abstractWe conclude the paper by extending a well-known Stone-type duality to the categories
dc.description.abstractof hypergraphs coupled with finite-based HP-morphisms and cone lattices
dc.description.abstractcoupled with frame homomorphisms that preserve compact elements.
dc.description.degreeM.S.
dc.identifier.urihttp://jewlscholar.mtsu.edu/xmlui/handle/mtsu/5660
dc.publisherMiddle Tennessee State University
dc.subject.umiMathematics
dc.thesis.degreegrantorMiddle Tennessee State University
dc.thesis.degreelevelMasters
dc.titleA Duality between hypergraphs and cone lattices
dc.typeThesis

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
French_mtsu_0170N_10930.pdf
Size:
565.75 KB
Format:
Adobe Portable Document Format
Download

Collections

Masters Theses