An alternative proof that Bing’s dogbone space is not topologically $E^{3}$
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- by E. H. Anderson
- Trans. Amer. Math. Soc. 150 (1970), 589-609
- DOI: https://doi.org/10.1090/S0002-9947-1970-0282351-2
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References
- J. W. Alexander, On the subdivision of $3$-space by a polyhedron, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 6-8.
E. H. Anderson, Some decompositions of ${E^3}$, Master’s Thesis, Louisiana State University, Baton Rouge, 1964.
E. H. Anderson, Two-spheres which avoid ${I^3}$ if ${I^3}$ contains a $p$-od, Duke Math. J. 36 (1969), 7-14. MR 38 #5190.
Steve Armentrout, Decompositions of ${E^3}$ with a compact $0$-dimensional set of nondegenerate elements, Trans. Amer. Math. Soc. 123 (1966), 165-177. MR 33 #3279.
R. H. Bing, A homeomorphism between the $3$-sphere and the sum of two solid horned spheres, Ann. of Math. (2) 56 (1952), 354-362. MR 14, 192.
—, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 456-483. MR 19, 300.
—, 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 19, 1187.
B. G. Casler, On the sum of two solid Alexander horned spheres, Trans. Amer. Math. Soc. 116 (1965), 135-150. MR 32 #3049.
J. G. Hocking and Gail S. Young, Topology, Addison-Wesley, Reading, Mass., 1961. MR 23 #A2857.
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 150 (1970), 589-609
- MSC: Primary 54.78
- DOI: https://doi.org/10.1090/S0002-9947-1970-0282351-2
- MathSciNet review: 0282351