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Proceedings of the American Mathematical Society

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A generalization of the dog bone space to $ E\sp{n}$


Author: W. T. Eaton
Journal: Proc. Amer. Math. Soc. 39 (1973), 379-387
MSC: Primary 57A15
DOI: https://doi.org/10.1090/S0002-9939-1973-0322877-4
MathSciNet review: 0322877
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Abstract: In this paper we construct an upper semicontinuous decomposition of $ {E^n}(n \geqq 3)$ into points and tame arcs such that the associated decomposition space is distinct from $ {E^n}$.


References [Enhancements On Off] (What's this?)

  • [1] M. L. Antoine, Sur l'homeomorphie de deux figures et de leurs voisinages, J. Math. Pures Appl. 86 (1921), 221-325.
  • [2] 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 19, 1187. MR 0092961 (19:1187g)
  • [3] -, A wild surface each of whose arcs is tame, Duke Math. J. 28 (1961), 1-15. MR 23 #A630. MR 0123302 (23:A630)
  • [4] W. A. Blankinship, Generalization of a construction of Antoine, Ann. of Math. (2) 53 (1951), 276-297. MR 12, 730. MR 0040659 (12:730c)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0322877-4
Keywords: Tame arcs, wild embeddings, cellular maps, upper semi-continuous
Article copyright: © Copyright 1973 American Mathematical Society

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