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

 

A $ 2$-sphere of vetical order $ 5$ bounds a $ 3$-cell


Author: L. D. Loveland
Journal: Proc. Amer. Math. Soc. 26 (1970), 674-678
MSC: Primary 54.78
MathSciNet review: 0268871
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Abstract: A subset $ X$ of $ {E^3}$ is said to have vertical order $ n$ if no vertical line contains more than $ n$ points of $ X$. We prove that each $ 2$-sphere in $ {E^3}$ which has vertical order 5 bounds a $ 3$-cell.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0268871-0
PII: S 0002-9939(1970)0268871-0
Keywords: Tame $ 2$-spheres, tame surfaces, embeddings in $ {E^3}$, surfaces in $ {E^3}$, $ \ast $-taming sets, vertical order
Article copyright: © Copyright 1970 American Mathematical Society