The classical and generalized Schoenflies theorems
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- David Lee Heatherly (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Richard B. Sher
Abstract: The classical Schoenflies Theorem states that for any Jordan 2 curve J in the Euclidean plane E2 , there exists a homeomorphism h of E2 onto itself such that h(J) - S1 . The generalized Schoenflies Theorem states that if h is a homeomorphic embedding of Sn-1 [0,1] into the standard n-sphere Sn , then the closure of either complementary domain of h(Sn-1 x {1/2}) is a topological n-cell. In this thesis, we will show that for any Jordan curve J in E2 there exists a homeomorphic embedding h:S1 x [0,1] into E2 such that h(S1 x {1/2} = J, thereby showing that the classical Schoenflies Theorem is a consequence of the generalized Schoenflies Theorem.
The classical and generalized Schoenflies theorems
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Created on 1/1/1977
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Additional Information
- Publication
- Thesis
- Language: English
- Date: 1977
- Subjects
- Jordan curves.
- Homeomorphisms
- Topological spaces