The Lattice of Equivalence Classes of Closed Sets and the Stone-Cech Compactification.

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dc.contributor.advisor Dr. Gary Faulkner, Committee Chair en_US
dc.contributor.advisor Dr. Richard Chandler, Committee Member en_US
dc.contributor.advisor Dr. Kailash Misra, Committee Member en_US
dc.contributor.advisor Dr. Ernest Stitzinger, Committee Member en_US Seaton, Gerald Arthur en_US 2010-04-02T18:45:19Z 2010-04-02T18:45:19Z 2005-03-16 en_US
dc.identifier.other etd-03022004-144221 en_US
dc.description.abstract βX X is the remainder of the Stone-Cech compactification of a locally compact space X. This paper introduces a lattice which we call L(X) that is constructed using equivalence classes of closed sets of X. We then determine that St(L(X)) (the set of ultrafilters on L(X)) is homeomorphic to βX X. We subsequently give some examples. Most notably, for X = H this now provides a lattice-theoretic approach for representing βH H. In addition, we expand and clarify some aspects of lattice theory related to our constructions. We introduce the term "upwardly nonlinear" as a way to describe lattices with a certain property related to the ultrafilters on it. We also investigate some of the lattice properties of L(X). en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject normal en_US
dc.subject pseudocomplement en_US
dc.subject disjunction en_US
dc.subject filter en_US
dc.subject Stone space en_US
dc.subject Boolean algebra en_US
dc.title The Lattice of Equivalence Classes of Closed Sets and the Stone-Cech Compactification. en_US PhD en_US dissertation en_US Mathematics en_US

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