Full metadata
Title
Proofs and Generalizations of the Jordan Curve Theorem
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.
Date Created
2020-05
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)
Topical Subject
Resource Type
Extent
60 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
Series
Academic Year 2019-2020
Handle
https://hdl.handle.net/2286/R.I.63121
Level of coding
minimal
Cataloging Standards
System Created
- 2021-02-12 04:42:35
System Modified
- 2021-08-11 04:09:57
- 3 years 3 months ago
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