A surface in 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 | References | Similar Articles | Additional Information

Abstract: R. H. Bing has asked if a -sphere in is tame when it is known that for each point in there exist two round balls which are tangent to each other at and which lie, except for , in opposite complementary domains of . 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 -spheres,
surfaces in ,
tangent round balls,
locally capped spheres,
characterizations of tameness

Article copyright:
© Copyright 1970
American Mathematical Society