Some results on Gδ ideals of compact sets

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Saran, Maya

Contributors dc:contributor

• Solecki, Slawomir
• Henson, C. Ward
• Kaufman, Robert
• Rosendal, Christian

• G-delta ideals
• ideals of compact sets

Statement dc:rights

• Copyright 2010 Maya Saran

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16935

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/16935