The classical and generalized Schoenflies theorems

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