Author

Aaron Fowlkes

Date of Award

Fall 2019

Document Type

Open Access Thesis

Department

Mathematics

First Advisor

Peter Nyikos

Abstract

The main focus of this paper is the concept of a moving off collection of sets. We will be looking at how this relatively lesser known idea connects and interacts with other more widely used topological properties. In particular we will examine how moving off collections act with the function spaces Cp(X), C0(X), and CK (X). We conclude with a chapter on the Cantor tree and its moving off connections.

Many of the discussions of important theorems in the literature are expressed in terms that do not suggest the concept of moving off but can be rephrased using it. The main goal of this paper is to bring these scattered pieces of information together into a single organized work. As a secondary goal we will endeavor to make a number of important theorems in the literature easier for non-specialists to understand by giving expanded versions of their existing proofs.

Included in

Mathematics Commons

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