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

Spheres in $ E\sp{3}$ which are homogeneous over a 0-dimensional set


Author: C. E. Burgess
Journal: Proc. Amer. Math. Soc. 63 (1977), 171-174
MSC: Primary 57A10
MathSciNet review: 0442942
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Abstract: A 2-sphere S in Euclidean 3-space $ {E^3}$ is defined to be homogeneous over the subset X of S if for each p, $ q \in X$ there is a homeomorphism $ h:{E^3} \to {E^3}$ such that $ h(S) = S$ and $ h(p) = q$. It is shown that a 2-sphere S in $ {E^3}$ is tame from one side provided S is locally tame modulo a tame 0-dimensional set C such that S is homogeneous over C. An example is described to show that it is necessary to require that C be tame.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0442942-4
PII: S 0002-9939(1977)0442942-4
Keywords: Tame spheres, homogeneous embeddings, horned spheres
Article copyright: © Copyright 1977 American Mathematical Society