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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



An improved version of the noncompact weak canonical Schoenflies theorem

Author: W. R. Brakes
Journal: Trans. Amer. Math. Soc. 213 (1975), 61-69
MSC: Primary 57A35
MathSciNet review: 0391103
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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.

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Keywords: Euclidean space, proper locally-flat embedding, canonical extension, compact-open topology, uniform topology, majorant topology
Article copyright: © Copyright 1975 American Mathematical Society