{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/16935"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/16935","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Some results on Gδ ideals of compact sets","abstract":"For a compact metric space E, Solecki has defined a broad natural class of G-delta ideals of compact sets on E, called G-delta 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 G-delta 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 G-delta ideals of compact sets on E, called G-delta 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 G-delta 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","Henson, C. 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Ward","Kaufman, Robert","Rosendal, Christian"],"dc:creator":["Saran, Maya"],"dc:date":["2010-08-20T18:02:21Z","2010-08"],"dc:description":["For a compact metric space E, Solecki has defined a broad natural class of G-delta ideals of compact sets on E, called G-delta 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. 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