The classical and generalized Schoenflies theorems

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
David Lee Heatherly (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
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.

Additional Information

Language: English
Date: 1977
Jordan curves.
Topological spaces

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