Tame boundary sets of crumpled cubes in 𝐸³

Lister, F. M.

doi:10.1090/S0002-9939-1970-0257999-7

Tame boundary sets of crumpled cubes in $E^{3}$
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by F. M. Lister

Proc. Amer. Math. Soc. 25 (1970), 377-378

DOI: https://doi.org/10.1090/S0002-9939-1970-0257999-7

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Abstract:

If a crumpled cube $K$ in ${E^3}$ is re-embedded by a homeomorphism $h$ such that $h(K)$ is tame from Ext $h(K)$ and $F$ is a tame closed subset of Bd $K$ which either has no degenerate components or consists entirely of degenerate components, then $h(F)$ is tame.

References

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J. W. Cannon, Characterization of taming sets on $2$-spheres, Trans. Amer. Math. Soc. 147 (1970), 289–299. MR 257996, DOI 10.1090/S0002-9947-1970-0257996-6
Robert J. Daverman, A new proof for the Hosay-Lininger theorem about crumpled cubes, Proc. Amer. Math. Soc. 23 (1969), 52–54. MR 246274, DOI 10.1090/S0002-9939-1969-0246274-4

The sum of a real cube and a crumpled cube is

10

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