Term of Award
Spring 2012
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
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
Research Data and Supplementary Material
No
