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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Tame polyhedra in wild cells and spheres


Author: R. B. Sher
Journal: Proc. Amer. Math. Soc. 30 (1971), 169-174
MSC: Primary 54.78
MathSciNet review: 0281178
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Abstract: It is shown that each arc on a disk D in $ {E^4}$ can be homeomorphically approximated by an arc in D which is tame in $ {E^4}$. Some applications of this are given. Also, we construct an everywhere wild $ (n - 1)$-sphere in $ {E^n},n \geqq 3$, each of whose arcs is tame in $ {E^n}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0281178-1
PII: S 0002-9939(1971)0281178-1
Keywords: Everywhere wild, homeomorphically approximate, disk squeezing, cellularity
Article copyright: © Copyright 1971 American Mathematical Society