We show that any Borel action on a standard Borel space of a group which is topologically isomorphic to the sum of a countable abelian group with a countable sum of lines and circles induces an orbit equivalence relation which is hypersmooth. We also show that any Borel action of a second countable locally compact abelian group on a standard Borel space induces an orbit equivalence relation which is essentially hyperfinite, generalizing a result of Gao and Jackson for the countable abelian groups.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc1505289 |
| Date | 05 1900 |
| Creators | Cotton, Michael R. |
| Contributors | Gao, Su, Jackson, Stephen C., Kallman, Robert R. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 48 pages, Text |
| Rights | Public, Cotton, Michael R., Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
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