Spheres in $E^{3}$ which are homogeneous over a $0$-dimensional set
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- by C. E. Burgess PDF
- Proc. Amer. Math. Soc. 63 (1977), 171-174 Request permission
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.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 171-174
- MSC: Primary 57A10
- DOI: https://doi.org/10.1090/S0002-9939-1977-0442942-4
- MathSciNet review: 0442942