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Transactions of the American Mathematical Society

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

 

 

A surface in $ E\sp{3}$ is tame if it has round tangent balls


Author: L. D. Loveland
Journal: Trans. Amer. Math. Soc. 152 (1970), 389-397
MSC: Primary 57.05
MathSciNet review: 0270381
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Abstract: R. H. Bing has asked if a $ 2$-sphere $ S$ in $ {E^3}$ is tame when it is known that for each point $ p$ in $ S$ there exist two round balls which are tangent to each other at $ p$ and which lie, except for $ p$, in opposite complementary domains of $ S$. The main result in this paper is that Bing's question has an affirmative answer.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0270381-6
Keywords: Tame surfaces, tame $ 2$-spheres, surfaces in $ {E^3}$, tangent round balls, locally capped spheres, characterizations of tameness
Article copyright: © Copyright 1970 American Mathematical Society