Haar systems on locally compact groupoids
| buir.advisor | Gheondea Eladi, Aurelian Bebe Nicu | |
| dc.contributor.author | Güleken, Ayşe Işıl | |
| dc.date.accessioned | 2022-08-22T12:02:14Z | |
| dc.date.available | 2022-08-22T12:02:14Z | |
| dc.date.copyright | 2022-07 | |
| dc.date.issued | 2022-07 | |
| dc.date.submitted | 2022-08-19 | |
| dc.department | Department of Mathematics | en_US |
| dc.description | Cataloged from PDF version of article. | en_US |
| dc.description | Thesis (Master's): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2022. | en_US |
| dc.description | Includes bibliographical references (leave 44-45). | en_US |
| dc.description.abstract | Haar systems are generalizations of Haar measures on groups to groupoids. Naturally, important research directions in the field try to generalize the well known existence of a Haar measure on a locally compact group to the existence of Haar systems in different groupoid settings. The groupoid case differs significantly from the group case, evidenced by a result of Deitmar, showing that non-existence is possible even for compact groupoids. We first present the classical theory of locally compact groups and Haar Measures on them. We motivate our investigation by constructing full C∗-algebras on locally compact groups, which uses the existence of Haar measures. Then, we cover the theory of locally compact groupoids and present Renault's result that provides a complete characterization of the existence of Haar systems for the r-discrete locally compact groupoid setting, which are precisely the ones where the range map is a local homeomorphism. We present a question from Williams that investigates if the open range map assumption is redundant for second countable, locally compact and transitive groupoids. Finally, we present Buneci's counter-example that answers this question in the negative. | en_US |
| dc.description.degree | M.S. | en_US |
| dc.description.statementofresponsibility | by Ayşe Işıl Güleken | en_US |
| dc.format.extent | vi, 45 leaves ; 30 cm. | en_US |
| dc.identifier.itemid | B161180 | |
| dc.identifier.uri | http://hdl.handle.net/11693/110462 | |
| dc.language.iso | English | en_US |
| dc.publisher | Bilkent University | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Haar systems | en_US |
| dc.subject | Locally compact groupoids | en_US |
| dc.subject | r-discrete groupoids | en_US |
| dc.title | Haar systems on locally compact groupoids | en_US |
| dc.title.alternative | Lokal kompakt grupoidlerde haar sistemleri | en_US |
| dc.type | Thesis | en_US |