Term of Award
Spring 2012
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Department
Department of Mathematical Sciences
Committee Chair
Fŕed́eric Mynard
Committee Member 1
Greg Michalski
Committee Member 2
Goran Lesaja
Abstract
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.
Recommended Citation
Farmer, Nathan Denton, "Compact Filters and the Arzelá-Ascoli Theorem" (2012). Electronic Theses and Dissertations. 675.
https://digitalcommons.georgiasouthern.edu/etd/675