Director of Research (if dissertation) or Advisor (if thesis)
Solecki, Slawomir
Doctoral Committee Chair(s)
Henson, C. Ward
Committee Member(s)
Solecki, Slawomir
Kaufman, Robert
Rosendal, Christian
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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