Joe Mashburn, Jonathan Brown
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.
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Lee, Wyatt N., "The Cantor Set, Trees, and Compact Metric Spaces" (2021). Honors Theses. 344.