An improved version of the noncompact weak canonical Schoenflies theorem

Brakes, W. R.

doi:10.1090/S0002-9947-1975-0391103-9

An improved version of the noncompact weak canonical Schoenflies theorem
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Trans. Amer. Math. Soc. 213 (1975), 61-69 Request permission

Abstract:

The main result of this paper is that any proper collared embedding of ${R^{n - 1}}$ in ${R^n}$ can be extended to a homeomorphism of ${R^n}$ such that the extension depends continuously on the original embedding in a stronger sense than previously known. Analogous results are proved for proper embeddings of ${R^k}$ in ${R^n}$ (with the usual homotopy conditions when $k = n - 2$). An alternative proof of the usual compact form of the weak canonical Schoenflies theorem is also obtained.

References

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