The Study of Translation Equivalence on Integer Lattices

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.

Grantor dc:publisher

University of North Texas

Year dc:date

2003

Author dc:creator

• Boykin, Charles Martin

Contributors dc:contributor

• Jackson, Stephen C.
• Gao, Su
• Clark, Alex

• Borel sets.
• Lattice theory.
• marker sets
• Integer lattices
• equivalence
• translation

Statement dc:rights

• Public
• Copyright
• Boykin, Charles Martin
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 53451586
https://digital.library.unt.edu/ark:/67531/metadc4345/
ark: ark:/67531/metadc4345

OAI identifier oai:identifier

info:ark/67531/metadc4345