A proof of the generalized Schoenflies theorem

The following problem has been of interest for some time : Suppose h is a homeomorphic embedding of S~~X [0l] in S. Are the closures of the complementary domains of h(S~Xl/2) topological w-cells? Recently, Barry Mazur [ l ] proved that the answer is affirmative if the embedding h satisfies a simple "niceness" condition. In this paper we prove that the answer is affirmative with no extra conditions on h required.