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https://hdl.handle.net/2142/86939
Description
Title
Some Results on G-Delta Ideals of Compact Sets
Author(s)
Saran, Maya
Issue Date
2010
Doctoral Committee Chair(s)
Solecki, Slawomir
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Theoretical Mathematics
Language
eng
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.
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