$^{\ast }$-taming sets for crumpled cubes. II. Horizontal sections in closed sets
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- by James W. Cannon PDF
- Trans. Amer. Math. Soc. 161 (1971), 441-446 Request permission
Abstract:
We prove that a closed subset X of ${E^3}$ is a $^ \ast$-taming set if no horizontal section of X has a degenerate component. This implies, for example, that a 2-sphere S in ${E^3}$ is tame if no horizontal section of S has a degenerate component. It also implies (less obviously) that a 2-sphere S in ${E^3}$ is tame if it can be touched at each point from each side of S by a pencil.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 161 (1971), 441-446
- MSC: Primary 54.78
- DOI: https://doi.org/10.1090/S0002-9947-1971-0282354-9
- MathSciNet review: 0282354