$^{\ast }$-taming sets for crumpled cubes. III. Horizontal sections in $2$-spheres
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- by James W. Cannon PDF
- Trans. Amer. Math. Soc. 161 (1971), 447-456 Request permission
Abstract:
We prove that a 2-sphere S in ${E^3}$ is tame if each horizontal section of S has at most four components. Since there are wild spheres in ${E^3}$ whose horizontal sections have at most five components, this result is, in a sense, best possible. Much can nevertheless be said, however, even if certain sections have more than five components; and we show that the wildness of a 2-sphere S in ${E^3}$ is severely restricted by the requirement that each of the horizontal sections of S have at most finitely many components that separate S.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 161 (1971), 447-456
- MSC: Primary 54.78
- DOI: https://doi.org/10.1090/S0002-9947-1971-0282355-0
- MathSciNet review: 0282355