Honors Theses
Advisor
Joe Mashburn, Jonathan Brown
Department
Mathematics
Publication Date
12-2021
Document Type
Honors Thesis
Abstract
The Cantor Set is a famous topological set developed from an infinite process of starting with the interval [0,1] and, at each iteration, removing the middle third of the intervals remaining. Our goal is to determine some of the properties of this unintuitive set and to show that it is homeomorphic to any general compact metric space with similar properties. To do so, we show that the Cantor Set is topologically equivalent to a tree, a more familiar structure, and use this fact to establish a homeomorphism to the general compact metric space.
Permission Statement
This item is protected by copyright law (Title 17, U.S. Code) and may only be used for noncommercial, educational, and scholarly purposes.
Keywords
Undergraduate research
eCommons Citation
Lee, Wyatt N., "The Cantor Set, Trees, and Compact Metric Spaces" (2021). Honors Theses. 344.
https://ecommons.udayton.edu/uhp_theses/344
COinS
