Self-universal crumpled cubes and a dogbone space

Anderson, E. H.

doi:10.1090/S0002-9939-1972-0310891-3

Self-universal crumpled cubes and a dogbone space
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by E. H. Anderson

Proc. Amer. Math. Soc. 36 (1972), 280-282

DOI: https://doi.org/10.1090/S0002-9939-1972-0310891-3

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Abstract:

The question of whether each self-universal crumpled cube is universal is answered negatively by presenting an example of a dogbone space which is not topologically ${E^3}$ but which can be expressed as a sewing of two crumpled cubes, one of which is self-universal.

References

E. H. Anderson, Chains of simple closed curves and a dogbone space, Fund. Math. 72 (1971), no. 2, 131–144. MR 295310, DOI 10.4064/fm-72-2-131-144
Charles D. Bass and Robert J. Daverman, A self-universal crumpled cube which is not universal, Bull. Amer. Math. Soc. 76 (1970), 740–742. MR 263050, DOI 10.1090/S0002-9904-1970-12529-0
R. H. Bing, A decomposition of $E^3$ into points and tame arcs such that the decomposition space is topologically different from $E^3$, Ann. of Math. (2) 65 (1957), 484–500. MR 92961, DOI 10.2307/1970058
C. E. Burgess and J. W. Cannon, Embeddings of surfaces in $E^{3}$, Rocky Mountain J. Math. 1 (1971), no. 2, 259–344. MR 278277, DOI 10.1216/RMJ-1971-1-2-259
B. G. Casler, On the sum of two solid Alexander horned spheres, Trans. Amer. Math. Soc. 116 (1965), 135–150. MR 185585, DOI 10.1090/S0002-9947-1965-0185585-9
W. T. Eaton, The sum of solid spheres, Michigan Math. J. 19 (1972), 193–207. MR 309116
John R. Stallings, Uncountably many wild disks, Ann. of Math. (2) 71 (1960), 185–186. MR 111003, DOI 10.2307/1969885