Tame boundary sets of crumpled cubes in
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
Abstract | References | Similar Articles | Additional Information
Abstract: If a crumpled cube in
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
, Pacific J. Math. 11 (1961), 435-446. MR 24 #A539. MR 0130679 (24:A539)
- [2]
J. W. Cannon, Characterization of taming sets on
-spheres, Trans. Amer. Math. Soc. 147 (1970), 289-299. MR 0257996 (41:2644)
- [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 (39:7578)
- [4]
Norman Hosay, The sum of a real cube and a crumpled cube is
, 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 31 #2717. MR 0178460 (31:2717)
- [6] F. M. Lister, Simplifying intersections of disks in Bing's side approximation theorem, Pacific J. Math. 22 (1967), 281-295. MR 35 #7317. MR 0216484 (35:7317)
- [7]
L. D. Loveland, Tame subsets of spheres in
, Pacific J. Math. 19 (1966), 489-517. MR 37 #903. MR 0225309 (37:903)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.78, 57.00
Retrieve articles in all journals with MSC: 54.78, 57.00
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1970-0257999-7
Keywords:
Crumpled cube,
tame closed 0-dimensional subset,
simple neighborhoods,
re-embedded in ,
tame from its exterior
Article copyright:
© Copyright 1970
American Mathematical Society