Some Results on G-Delta Ideals of Compact Sets

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.

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

2015

Author dc:creator

• Saran, Maya

Contributors dc:contributor

• Solecki, Slawomir

• Theoretical Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3452263

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86939