{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86939"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86939","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Some Results on G-Delta Ideals of Compact Sets","abstract":"For a compact metric space E, Solecki has defined a broad natural class of Gdelta ideals of compact sets on E, called Gdelta ideals with property (*), and has shown that any ideal I in this class can be represented through the ideal of nowhere dense subsets of a closed subset F of the hyperspace of compact subsets of E. In this thesis we show that the closed set F in this representation can be taken to be closed upwards, i.e., it contains the compact supersets of its members. We examine the behaviour of Gdelta subsets of E with respect to the representing sets of I; we formulate a conjecture and prove it for several classes of ideals.","abstract_html":"For a compact metric space E, Solecki has defined a broad natural class of Gdelta ideals of compact sets on E, called Gdelta ideals with property (*), and has shown that any ideal I in this class can be represented through the ideal of nowhere dense subsets of a closed subset F of the hyperspace of compact subsets of E. In this thesis we show that the closed set F in this representation can be taken to be closed upwards, i.e., it contains the compact supersets of its members. We examine the behaviour of Gdelta subsets of E with respect to the representing sets of I; we formulate a conjecture and prove it for several classes of ideals.","abstract_has_math":false,"creators":["Saran, Maya"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Solecki, Slawomir"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:15Z","date_published":"2015-09-28T15:20:15Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Theoretical Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3452263"],"render_values":[{"text":"(MiAaPQ)AAI3452263","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86939","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Solecki, Slawomir"]},{"key":"dc:creator","label":"Author","values":["Saran, Maya"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:15Z","10000-01-01","2010"]},{"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":["Theoretical Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86939","(MiAaPQ)AAI3452263"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["For a compact metric space E, Solecki has defined a broad natural class of Gdelta ideals of compact sets on E, called Gdelta ideals with property (*), and has shown that any ideal I in this class can be represented through the ideal of nowhere dense subsets of a closed subset F of the hyperspace of compact subsets of E. 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In this thesis we show that the closed set F in this representation can be taken to be closed upwards, i.e., it contains the compact supersets of its members. We examine the behaviour of Gdelta subsets of E with respect to the representing sets of I; we formulate a conjecture and prove it for several classes of ideals.","Made available in DSpace on 2015-09-28T15:20:15Z (GMT). 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