Vol. 32, No. 2, 1970

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Extending homeomorphisms

Jerome L. Paul

Vol. 32 (1970), No. 2, 517–520

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.

Mathematical Subject Classification
Primary: 57.01
Received: 8 October 1968
Published: 1 February 1970
Jerome L. Paul