Theorem 1 of this paper
establishes a necessary and sufficient condition that a locally flat imbedding
f : Bk→ Rn of a k-cell in euclidean n-space Rn admits an extension to a
homeomorphism F : Rn→ Rn onto Rn such that F|(Rn− Bk) is a diffeomorphism
which is the identity outside some compact set in Rn. An analogous result for locally
flat imbeddings of a euclidean (n − 1)-sphere into Rn is proved. A lemma which
generalizes a theorem of Huebsch and Morse concerning Schoenflies extensions
without interior differential singularities is also established.
