-taming sets for crumpled cubes. II. Horizontal sections in closed sets

Author:
James W. Cannon

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

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that a closed subset *X* of is a -taming set if no horizontal section of *X* has a degenerate component. This implies, for example, that a 2-sphere *S* in is tame if no horizontal section of *S* has a degenerate component. It also implies (less obviously) that a 2-sphere *S* in is tame if it can be touched at each point from each side of *S* by a pencil.

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DOI:
https://doi.org/10.1090/S0002-9947-1971-0282354-9

Keywords:
Taming sets,
-taming sets,
slices in 2-spheres,
surfaces in 3-manifolds,
2-spheres in

Article copyright:
© Copyright 1971
American Mathematical Society