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 $E\sp{3}$

Author: F. M. Lister
Journal: Proc. Amer. Math. Soc. 25 (1970), 377-378
MSC: Primary 54.78; Secondary 57.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0257999-7
MathSciNet review: 0257999
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

[1] R. H. Bing, Tame Cantor sets in 𝐸³, Pacific J. Math. 11 (1961), 435–446. MR 0130679
[2] J. W. Cannon, Characterization of taming sets on 2-spheres, Trans. Amer. Math. Soc. 147 (1970), 289–299. MR 0257996, https://doi.org/10.1090/S0002-9947-1970-0257996-6
[3] Robert J. Daverman, A new proof for the Hosay-Lininger theorem about crumpled cubes, Proc. Amer. Math. Soc. 23 (1969), 52–54. MR 0246274, https://doi.org/10.1090/S0002-9939-1969-0246274-4
[4] Norman Hosay, The sum of a real cube and a crumpled cube is ${S^3}$ , Notices Amer. Math. Soc. 10 (1963), 668. Abstract #607-17.
[5] Lloyd L. Lininger, Some results on crumpled cubes, Trans. Amer. Math. Soc. 118 (1965), 534–549. MR 0178460, https://doi.org/10.1090/S0002-9947-1965-0178460-7
[6] F. M. Lister, Simplifying intersections of disks in Bing’s side approximation theorem, Pacific J. Math. 22 (1967), 281–295. MR 0216484
[7] L. D. Loveland, Tame subsets of spheres in 𝐸³, Pacific J. Math. 19 (1966), 489–517. MR 0225309

Bibliography