Dissertation/Thesis Abstract

A Duality Between Hypergraphs and Cone Lattices
by French, Zack, M.S., Middle Tennessee State University, 2018, 126; 10784141
Abstract (Summary)

In this paper, we introduce and characterize the class of lattices that arise as the family of lowersets of the incidence poset for a hypergraph. In particular, we show that the following statements are logically equivalent: 1. A lattice L is order isomorphic to the frame of opens for a hypergraph endowed with the Classical topology. 2. A lattice L is bialgebraic, distributive, and its subposet of completely joinprime elements forms the incidence poset for a hypergraph. 3. A lattice L is a cone lattice.

We conclude the paper by extending a well-known Stone-type duality to the categories of hypergraphs coupled with finite-based HP-morphisms and cone lattices coupled with frame homomorphisms that preserve compact elements.

Indexing (document details)
Advisor: Hart, James B.
Commitee: Sarkar, Medha, Ye, Dong
School: Middle Tennessee State University
Department: College of Basic & Applied Sciences
School Location: United States -- Tennessee
Source: MAI 57/05M(E), Masters Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics
Keywords:
Publication Number: 10784141
ISBN: 9780355931013
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