Description
The Jordan curve theorem states that any homeomorphic copy of a circle into R2 divides the plane into two distinct regions. This paper reconstructs one proof of the Jordan curve theorem before turning its attention toward generalizations of the theorem and their proofs and counterexamples. We begin with an introduction to elementary topology and the different notions of the connectedness of a space before constructing the first proof of the Jordan curve theorem. We then turn our attention to algebraic topology which we utilize in our discussion of the Jordan curve theorem’s generalizations. We end with a proof of the Jordan-Brouwer theorems, extensions of the Jordan curve theorem to higher dimensions.
Details
Title
- Proofs and Generalizations of the Jordan Curve Theorem
Contributors
- Clark, Kacey (Author)
- Kawski, Matthias (Thesis director)
- Paupert, Julien (Committee member)
- Department of Physics (Contributor)
- School of Mathematical and Statistical Sciences (Contributor)
- Barrett, The Honors College (Contributor)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2020-05
Subjects
Resource Type
Collections this item is in