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Some results on Gδ ideals of compact sets

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Title: Some results on Gδ ideals of compact sets
Author(s): Saran, Maya
Director of Research: Solecki, Slawomir
Doctoral Committee Chair(s): Henson, Ward
Doctoral Committee Member(s): Solecki, Slawomir; Kaufman, Robert; Rosendal, Christian
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): G-delta ideals 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.
Issue Date: 2010-08-20
Rights Information: Copyright 2010 Maya Saran
Date Available in IDEALS: 2010-08-20
Date Deposited: 2010-08

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