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.

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