Tame polyhedra in wild cells and spheres

Sher, R. B.

doi:10.1090/S0002-9939-1971-0281178-1

Tame polyhedra in wild cells and spheres
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by R. B. Sher

Proc. Amer. Math. Soc. 30 (1971), 169-174

DOI: https://doi.org/10.1090/S0002-9939-1971-0281178-1

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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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