{"id":{"repo_id":"unt","oai_identifier":"info:ark/67531/metadc4345"},"canonical_url":"https://search.dev.ndltd.org/etd/unt/info:ark/67531/metadc4345","repository":{"repo_id":"unt","name":"University of North Texas","base_url":"https://digital.library.unt.edu/oai/"},"display":{"title":"The Study of Translation Equivalence on Integer Lattices","abstract":"This paper is a contribution to the study of countable Borel equivalence relations on standard Borel spaces. We concentrate here on the study of the nature of translation equivalence. We study these known hyperfinite spaces in order to gain insight into the approach necessary to classify certain variables as either being hyperfinite or not. In Chapter 1, we will give the basic definitions and examples of spaces used in this work. The general construction of marker sets is developed in this work. These marker sets are used to develop several invariant tilings of the equivalence classes of specific variables . Some properties that are equivalent to hyperfiniteness in the certain space are also developed. Lastly, we will give the new result that there is a continuous injective embedding from certain defined variables.","abstract_html":"This paper is a contribution to the study of countable Borel equivalence relations on standard Borel spaces. We concentrate here on the study of the nature of translation equivalence. We study these known hyperfinite spaces in order to gain insight into the approach necessary to classify certain variables as either being hyperfinite or not. In Chapter 1, we will give the basic definitions and examples of spaces used in this work. The general construction of marker sets is developed in this work. These marker sets are used to develop several invariant tilings of the equivalence classes of specific variables . Some properties that are equivalent to hyperfiniteness in the certain space are also developed. Lastly, we will give the new result that there is a continuous injective embedding from certain defined variables.","abstract_has_math":false,"creators":["Boykin, Charles Martin"],"institution":"University of North Texas","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Jackson, Stephen C.","Gao, Su","Clark, Alex"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-08","date_published":"2003-08","updated_at":"2026-07-24T05:35:09Z","subjects":["Borel sets.","Lattice theory.","marker sets","Integer lattices","equivalence","translation"],"languages":["English"],"rights":["Public","Copyright","Boykin, Charles Martin","Copyright is held by the author, unless otherwise noted. All rights reserved."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["oclc: 53451586","https://digital.library.unt.edu/ark:/67531/metadc4345/","ark: ark:/67531/metadc4345"],"render_values":[{"text":"oclc: 53451586","href":null,"code":true},{"text":"https://digital.library.unt.edu/ark:/67531/metadc4345/","href":"https://digital.library.unt.edu/ark:/67531/metadc4345/","code":true},{"text":"ark: ark:/67531/metadc4345","href":null,"code":true}]}]},"links":{"outbound_url":"https://doi.org/10.12794/metadc4345","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jackson, Stephen C.","Gao, Su","Clark, Alex"]},{"key":"dc:creator","label":"Author","values":["Boykin, Charles Martin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2003-08"]},{"key":"dc:publisher","label":"Institution","values":["University of North Texas"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Borel sets.","Lattice theory.","marker sets","Integer lattices","equivalence","translation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["Public","Copyright","Boykin, Charles Martin","Copyright is held by the author, unless otherwise noted. 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The general construction of marker sets is developed in this work. These marker sets are used to develop several invariant tilings of the equivalence classes of specific variables . Some properties that are equivalent to hyperfiniteness in the certain space are also developed. Lastly, we will give the new result that there is a continuous injective embedding from certain defined variables."],"dc:format":["Text"],"dc:identifier":["oclc: 53451586","doi: 10.12794/metadc4345","https://digital.library.unt.edu/ark:/67531/metadc4345/","ark: ark:/67531/metadc4345"],"dc:language":["English"],"dc:publisher":["University of North Texas"],"dc:rights":["Public","Copyright","Boykin, Charles Martin","Copyright is held by the author, unless otherwise noted. All rights reserved."],"dc:subject":["Borel sets.","Lattice theory.","marker sets","Integer lattices","equivalence","translation"],"dc:title":["The Study of Translation Equivalence on Integer Lattices"],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:35:09Z"}