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Extending embeddings of Rn−1 in Rn

Published online by Cambridge University Press:  24 October 2008

Anthony Smith
Anthony Smith
Affiliation:
University of Durham and Trinity College, Cambridge
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Extract

Notation and results. The main results of this paper are (a) a new proof of the canonical Schoenflies theorem and (b) a non-compact version of the canonical Schoen-flies theorem.

The result (a) is already known(5); the existing proof is based on the proof by Brown of the ordinary Schoenflies theorem, whereas ours is based on that of Mazur and Morse.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 1 , January 1972 , pp. 5 - 18
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Cantrell, J. C.Separation of the n-sphere by an (n – l)-sphere. Trans. Amer. Math. Soc. 108 (1963), 185–194.Google Scholar
(2)Kirby, R. C.Topological manifolds. Graduate Lecture Course (Cambridge, 1970).Google Scholar
(3)Mazur, B.On embedding of spheres. Bull. Amer. Math. Soc. 65 (1959), 59–65.CrossRefGoogle Scholar
(4)Morse, M.A reduction of the Schoenflies extension problem. Bull. Amer. Math. Soc. 66 (1960) 113–115.CrossRefGoogle Scholar
(5)Huebsch, W. and Morse, M.The dependence of the Schoenflies extension on an accessory parameter (the topological case). Proc. Nat. Acad. Sci. 50 (1963), 1036–1037.CrossRefGoogle Scholar