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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A class of embeddings of $ S\sp{n-1}$ and $ B\sp{n}$ in $ R\sp{n}$


Authors: J. C. Cantrell, T. M. Price and T. B. Rushing
Journal: Proc. Amer. Math. Soc. 29 (1971), 208-210
MSC: Primary 57.05
DOI: https://doi.org/10.1090/S0002-9939-1971-0275445-5
MathSciNet review: 0275445
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Abstract: We show that if D is an n or $ (n - 1)$-cell in $ {R^n},n > 4$, and E is an $ (n - 2)$-cell in Bd D, with $ D - E$ locally flat in $ {R^n}$ and E locally flat in each of Bd D and $ {R^n}$, then D is locally flat in $ {R^n}$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0275445-5
Keywords: Local flatness, collared submanifolds, 1-SS, 1-LC
Article copyright: © Copyright 1971 American Mathematical Society