Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ \sp{\ast} $-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
MathSciNet review: 0282354
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54.78

Retrieve articles in all journals with MSC: 54.78


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0282354-9
PII: S 0002-9947(1971)0282354-9
Keywords: Taming sets, $ ^ \ast $-taming sets, slices in 2-spheres, surfaces in 3-manifolds, 2-spheres in $ {E^3}$
Article copyright: © Copyright 1971 American Mathematical Society