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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Neighborhoods of points in codimension-one submanifolds lie in codimension-one spheres


Author: Fredric D. Ancel
Journal: Proc. Amer. Math. Soc. 103 (1988), 1315-1316
MSC: Primary 57N35
MathSciNet review: 955028
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Abstract: For $ n \geq 4$, let $ M$ be an $ (n - 1)$-manifold embedded in an $ n$-manifold $ N$. For each point $ p$ of $ M$, there is an $ (n - 1)$-sphere $ \Sigma $ in $ N$ such that $ \Sigma \cap M$ is a neighborhood of $ p$ in $ M$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0955028-4
PII: S 0002-9939(1988)0955028-4
Article copyright: © Copyright 1988 American Mathematical Society