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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, C. 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
URI:http://hdl.handle.net/2142/16935
Rights Information:Copyright 2010 Maya Saran
Date Available in IDEALS:2010-08-20
Date Deposited:2010-08


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