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$ (E\sp{3}/X)\times E\sp{1}\approx E\sp{4}$ ($ X$, a cell-like set): an alternative proof


Author: J. W. Cannon
Journal: Trans. Amer. Math. Soc. 240 (1978), 277-285
MSC: Primary 57A15
DOI: https://doi.org/10.1090/S0002-9947-1978-0482770-2
MathSciNet review: 0482770
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Abstract: The author gives an alternative proof that a cell-like closed-0dimensional decomposition of $ {E^3}$ is an $ {E^4}$ factor. The argument is essentially 2-dimensional. The 3- and 4-dimensional topology employed is truly minimal.


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

  • [1] J. W. Cannon, Taming cell-like embedding relations, Geometric Topology (Proc. of the Geometric Topology Conf., Park City, February 19-22, 1974), edited by L. C. Glaser and T. B. Rushing, Springer-Verlag, Berlin and New York, 1975, pp. 66-118. MR 52 # 11926. MR 0391104 (52:11926)
  • [2] C. Pixley and W. Eaton, $ {S^1}$ cross a UV decomposition of $ {S^3}$ yields $ {S^1} \times {S^3}$, (Proc. of the Geometric Topology Conf., Park City, Utah, February 19-22, 1974), edited by L. C. Glaser and T. B. Rushing, Springer-Verlag, Berlin and New York, 1975, pp. 166-194. MR 52 # 15472. MR 0394672 (52:15473)
  • [3] R. D. Edwards and R. T. Miller, Cell-like closed 0-dimensional decompositions of $ {R^3}$ are $ {R^4}$ factors, Trans. Amer. Math. Soc. 215 (1976), 191-203. MR 0383411 (52:4292)
  • [4] D. R. McMillan, Jr., Compact, acyclic subsets of three-manifolds, Michigan Math. J. 16 (1969), 129-136. MR 39 #4822. MR 0243501 (39:4822)
  • [5] J. H. C. Whitehead, A certain open manifold whose group is unity, Quart. J. Math. (2) 6 (1935), 268-279.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0482770-2
Keywords: Cell-like set, cellular set, decomposition space, manifold factor, generalized manifold, cell-like relation
Article copyright: © Copyright 1978 American Mathematical Society

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