Compact Filters and the Arzelá-Ascoli Theorem

The Arzelà-Ascoli Theorem gives conditions for a set to be compact in a function space, and is a useful theorem for existence proofs in many different mathematical contexts. The most natural structure for Arzelà-Ascoli type theorems is the continuous convergence - which is not necessarily topological even if the underlying base spaces are. Compact filters, on the other hand, are the logical extension of compact sets to filters with similar compactness-type properties. Compact filters have proved to be a useful tool in optimization and analysis. This thesis will show conditions for a filter to be compact on a function space, thus establishing an Arzelà-Ascoli type of result for filters.

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2012

Author dc:creator

• Farmer, Nathan Denton

Contributors dc:contributor

• Greg Michalski
• Goran Lesaja

• ETD
• Arzelá-Ascoli
• Compact filters
• Convergence spaces
• Function spaces
• Filters
• Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/675

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1675