A Duality between hypergraphs and cone lattices

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dc.contributor.advisor Hart, James
dc.contributor.author French, Zack
dc.contributor.committeemember Sarkar, Medha
dc.contributor.committeemember Ye, Dong
dc.contributor.department Basic & Applied Sciences en_US
dc.date.accessioned 2018-06-05T20:04:52Z
dc.date.available 2018-06-05T20:04:52Z
dc.date.issued 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.description.degree M.S.
dc.identifier.uri http://jewlscholar.mtsu.edu/xmlui/handle/mtsu/5660
dc.publisher Middle Tennessee State University
dc.subject.umi Mathematics
dc.thesis.degreegrantor Middle Tennessee State University
dc.thesis.degreelevel Masters
dc.title A Duality between hypergraphs and cone lattices
dc.type Thesis
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