2026-09-21T05:52:43Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/117798 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Tserunyan, Anush Solecki, Sławomir Albin, Pierre Oikhberg, Timur 2022-12 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms The student, Dakota Ihli, accepted the attached license on 2022-11-29 at 15:03. The student, Dakota Ihli, submitted this Dissertation for approval on 2022-11-29 at 16:48. This Dissertation was approved for publication on 2022-12-02 at 13:00. DSpace SAF Submission Ingestion Package generated from Vireo submission #18670 on 2023-04-12 at 07:35:40 Describing generic elements of Polish groups Ihli, Dakota Thor 2022-12-02 Polish Groups Generic Elements Conjugacy Classes Automorphism Groups Random Poset Absolutely Continuous Topological Rank For a Polish group G, we say an element g ∈ G is generic if it has a comeagre conjugacy class. We examine the questions of existence, and of behavior, for generic elements in two particular Polish groups. Firstly, we give a concrete model-theoretic characterization of the generic automorphism of the countable universal ultrahomogeneous partial order, also called the random poset. Secondly, we prove that the group of order-preserving, absolutely continuous homeomorphisms of the interval admits generic elements, and we give a concrete characterization. Additionally, we show that this group is generically topologically 2-generated; that is, for a comeagre set of pairs (f,g) of absolutely continuous interval homeomorphisms, the subgroup <f,g> is dense. Thesis eng https://hdl.handle.net/2142/117798 Copyright 2022 Dakota Thor Ihli Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics