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Decompostions of $ E\sp{3}$ with a compact $ {\rm O}$-dimensional set of nondegenerate elements


Author: Steve Armentrout
Journal: Trans. Amer. Math. Soc. 123 (1966), 165-177
MSC: Primary 54.78
DOI: https://doi.org/10.1090/S0002-9947-1966-0195074-4
MathSciNet review: 0195074
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  • [1] S. Armentrout, Upper semi-continuous decompositions of $ E^{3}$ with at most countably many non-degenerate elements, Ann. of Math. 78 (1963), 605-618. MR 0156331 (27:6255)
  • [2] -, Concerning point-like decompositions of $ {S^3}$ that yield $ 3$-manifolds, Abstract 619-115, Notices Amer. Math. Soc. 12 (1965), 90.
  • [3] R. J. Bean, Decompositions of $ {E^3}$ which yield $ {E^3}$, Abstract 619-198, Notices Amer. Math. Soc. 12 (1965), 117.
  • [4] R. H. Bing, Upper semicontinuous decompositions of $ {E^3}$, Ann. of Math. 65 (1957), 363-374. MR 0092960 (19:1187f)
  • [5] -, A decomposition of $ {E^3}$ into points and tame arcs such that the decomposition space is topologically different from $ {E^3}$, Ann. of Math. 65 (1957), 484-500. MR 0092961 (19:1187g)
  • [6] -, A homeomorphism between the $ 3$-sphere and the sum of two solid horned spheres, Ann. of Math. 59 (1952), 354-362.
  • [7] -, Point like decompositions of $ {E^2}$, Fund. Math. 50 (1962), 431-453.
  • [8] -, Snake-like continua, Duke Math. J. 18 (1951), 653-663. MR 0043450 (13:265a)
  • [9] -, Inequivalent families of periodic homeomorphisms of $ {E^3}$, Ann. of Math. 80 (1964), 78-93. MR 0163308 (29:611)
  • [10] -, Topology of $ 3$-manifolds and related topics, Decompositions of $ {E^3}$, Prentice-Hall, Englewood Cliffs, N.J., 1962; pp. 5-21.
  • [11] -, An alternative proof that $ 3$-manifolds can be triangulated, Ann. of Math. 69 (1959), 37-65. MR 0100841 (20:7269)
  • [12] K. W. Kwun, Upper semi-continuous decompositions of the $ n$-sphere, Proc. Amer. Math. Soc. 13 (1962), 284-290.
  • [13] K. W. Kwun and F. Raymond, Almost acyclic maps of manifolds, Amer. J. Math. 86 (1964), 638-650. MR 0184239 (32:1712)
  • [14] L.L. Lininger, The sum of two crumpledcubes is $ {S^3}$ if it is a $ 3$-manifold, Abstract 64T-445, Notices Amer. Math. Soc. 11 (1964), 678.
  • [15] L. F. McAuley, Another decomposition of $ {E^3}$ into points and intervals (to appear).
  • [16] E. E. Moise, Affine structures in $ 3$-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. 56 (1952), 92-114. MR 0048805 (14:72d)
  • [17] R. L. Moore, Foundations of point set theory, rev. ed., Amer. Math. Soc. Colloq. Publ. Vol. 13, Amer. Math. Soc., Providence, R. I., 1962, MR 0150722 (27:709)
  • [18] C. D. Papakyriakopoulos, On Dehn's lemma and the asphericity of knots, Ann. of Math. 66 (1957), 1-250. MR 0090053 (19:761a)
  • [19] T. M. Price, Cellular decompositions of $ {E^3}$, Ph. D. Thesis, University of Wisconsin, Madison, Wis., 1964.
  • [20] H. Schubert, Knoten und Vollringe, Acta Math. 90 (1953), 132-286. MR 0072482 (17:291d)
  • [21] D. G. Stewart, Cellular subsets of the $ 3$-sphere, Trans. Amer. Math. Soc. 114 (1965), 10-22. MR 0173244 (30:3457)

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DOI: https://doi.org/10.1090/S0002-9947-1966-0195074-4
Article copyright: © Copyright 1966 American Mathematical Society

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