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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Keywords: Everywhere wild, homeomorphically approximate, disk squeezing, cellularity
Article copyright: © Copyright 1971 American Mathematical Society