{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/30971"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/30971","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Extending partial isomorphisms","abstract":"There are two main topics in the thesis. In the second chapter we study two-dimensional classes of topological similarity in the groups of automorphisms of some linearly ordered Fraisse classes: the rationals, the linearly ordered random graph and the linearly ordered Urysohn space. The main theorem establishes meagerness of two-dimensional similarity classes in these groups. As a byproduct we get some results about the group of isometries of the Urysohn space. The third chapter is devoted to the metrics on the free products and HNN extensions of groups with two-sided invariant metrics. Using the approach of Graev to metrics on the free groups we show the existence of the coproducts in the category of groups with two-sided invariant metrics and Lipschitz homomorphisms. We then apply this theory to formulate a criterion when two topologically similar elements in a SIN Polish group are conjugate inside a bigger SIN Polish group.","abstract_html":"There are two main topics in the thesis. In the second chapter we study two-dimensional classes of topological similarity in the groups of automorphisms of some linearly ordered Fraisse classes: the rationals, the linearly ordered random graph and the linearly ordered Urysohn space. The main theorem establishes meagerness of two-dimensional similarity classes in these groups. As a byproduct we get some results about the group of isometries of the Urysohn space. The third chapter is devoted to the metrics on the free products and HNN extensions of groups with two-sided invariant metrics. Using the approach of Graev to metrics on the free groups we show the existence of the coproducts in the category of groups with two-sided invariant metrics and Lipschitz homomorphisms. We then apply this theory to formulate a criterion when two topologically similar elements in a SIN Polish group are conjugate inside a bigger SIN Polish group.","abstract_has_math":false,"creators":["Slutskyy, Kostyantyn"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rosendal, Christian","van den Dries, Lou","Solecki, Slawomir","Kapovitch, Ilia"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-22T00:19:13Z","date_published":"2012-05-22T00:19:13Z","updated_at":"2026-07-22T22:25:29Z","subjects":["Polish groups","Graev metrics","topological similarity","induced conjugacy classes","Urysohn space"],"languages":["en"],"rights":["Copyright 2012 Kostyantyn Slutskyy"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/30971","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rosendal, Christian","van den Dries, Lou","Solecki, Slawomir","Kapovitch, Ilia"]},{"key":"dc:creator","label":"Author","values":["Slutskyy, Kostyantyn"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-05-22T00:19:13Z","2012-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Polish groups","Graev metrics","topological similarity","induced conjugacy classes","Urysohn space"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2012 Kostyantyn Slutskyy"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/30971"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["There are two main topics in the thesis. In the second chapter we study two-dimensional classes of topological similarity in the groups of automorphisms of some linearly ordered Fraisse classes: the rationals, the linearly ordered random graph and the linearly ordered Urysohn space. The main theorem establishes meagerness of two-dimensional similarity classes in these groups. As a byproduct we get some results about the group of isometries of the Urysohn space. The third chapter is devoted to the metrics on the free products and HNN extensions of groups with two-sided invariant metrics. Using the approach of Graev to metrics on the free groups we show the existence of the coproducts in the category of groups with two-sided invariant metrics and Lipschitz homomorphisms. We then apply this theory to formulate a criterion when two topologically similar elements in a SIN Polish group are conjugate inside a bigger SIN Polish group.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-03-28T19:10:17Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Slutskyy_Kostyantyn.pdf: 659136 bytes, checksum: 5f84f620b8262dc8f7e27da4840da836 (MD5)","Made available in DSpace on 2012-05-22T00:19:13Z (GMT). No. of bitstreams: 2 Slutskyy_Kostyantyn.pdf: 659136 bytes, checksum: 5f84f620b8262dc8f7e27da4840da836 (MD5) license.txt: 4069 bytes, checksum: 2e0ac00d76e3a50694782615d5931fd5 (MD5)"]},{"key":"dc:title","label":"Title","values":["Extending partial isomorphisms"]}]}],"canonical_facts":{"dc:contributor":["Rosendal, Christian","van den Dries, Lou","Solecki, Slawomir","Kapovitch, Ilia"],"dc:creator":["Slutskyy, Kostyantyn"],"dc:date":["2012-05-22T00:19:13Z","2012-05"],"dc:description":["There are two main topics in the thesis. In the second chapter we study two-dimensional classes of topological similarity in the groups of automorphisms of some linearly ordered Fraisse classes: the rationals, the linearly ordered random graph and the linearly ordered Urysohn space. The main theorem establishes meagerness of two-dimensional similarity classes in these groups. As a byproduct we get some results about the group of isometries of the Urysohn space. The third chapter is devoted to the metrics on the free products and HNN extensions of groups with two-sided invariant metrics. Using the approach of Graev to metrics on the free groups we show the existence of the coproducts in the category of groups with two-sided invariant metrics and Lipschitz homomorphisms. We then apply this theory to formulate a criterion when two topologically similar elements in a SIN Polish group are conjugate inside a bigger SIN Polish group.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-03-28T19:10:17Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Slutskyy_Kostyantyn.pdf: 659136 bytes, checksum: 5f84f620b8262dc8f7e27da4840da836 (MD5)","Made available in DSpace on 2012-05-22T00:19:13Z (GMT). No. of bitstreams: 2 Slutskyy_Kostyantyn.pdf: 659136 bytes, checksum: 5f84f620b8262dc8f7e27da4840da836 (MD5) license.txt: 4069 bytes, checksum: 2e0ac00d76e3a50694782615d5931fd5 (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/30971"],"dc:language":["en"],"dc:rights":["Copyright 2012 Kostyantyn Slutskyy"],"dc:subject":["Polish groups","Graev metrics","topological similarity","induced conjugacy classes","Urysohn space"],"dc:title":["Extending partial isomorphisms"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:29Z"}