Pacific Journal of Mathematics

Non-cell-like decompositions of $S^{3}$.

D. S. Coram and P. F. Duvall

Article information

Pacific J. Math., Volume 115, Number 1 (1984), 47-55.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N12: Topology of $E^3$ and $S^3$ [See also 57M40]
Secondary: 54B15: Quotient spaces, decompositions


Coram, D. S.; Duvall, P. F. Non-cell-like decompositions of $S^{3}$. Pacific J. Math. 115 (1984), no. 1, 47--55.

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  • [Bl] R. H.Bing, The Klinesphere characterization problem,Bull. Amer. Math. Soc, 52 (1946), 644-653.
  • [B2] R. H.Bing,A homeomorphism between the 3-sphere and thesum of two solid horned spheres, Ann. ofMath., 56(1952), 354-362.
  • [Bo] K.Borsuk, Theory ofShape,Polish Scientific Publishers, Warsaw, 1975.
  • [Col] D.Coram, ApproximateFibrations --A Geometric Perspective, Shape Theory and Geometric Topology, Lecture Notes in Mathematics, No. 870, Springer-Verlag, Berlin, 1981,37-47.
  • [CD1] D. Coram and P.Duvall, ApproximateFibrations, Rocky Mountain J. Math., 7 (1977),275-288.
  • [CD2] D. Coram and P.Duvall, Approximate fibrations and a movability condition for maps, Pacific J. Math., 72(1977), 41-56.
  • [CD3] D. Coram and P.Duvall, Mappings from S3 toS2 whosepoint inverses have theshape ofacircle, General Topology Appl., 10(1979), 239-246.
  • [CD4] D. Coram and P.Duvall, Non-degenerate k-sphere mappings, Topology Proceedings, 4 (1979), 67-82.
  • [CD5] D. Coram and P.Duvall, Finiteness theorems for approximate fibrations, Trans. Amer. Math. Soc, 269(1982), 383-394.
  • [CD6] D. Coram and P.Duvall, Local n-connectivity and approximate lifting, preprint.
  • [DS] J. Dydak and J. Segal, Shape Theory, Lecture notes in Math., Volume 688, Springer-Verlag, NewYork, 1978.
  • [EG] D. A. Edwards and Ross Geoghegan, The stability problem in shape and a Whitehead theorem inpro-homotopy, Trans. Amer. Math. Soc,214(1975), 261-277.
  • [HY] J. G. Hocking and G. S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass. (1961).
  • [H] S. T. Hu, Theory of Retracts, Wayne State University Press, Detroit,1965.
  • [KW] George Kozlowski and John L. Walsh, The cell-like mapping problem, Bull. Amer. Math. Soc,2 (1980), 315-316.
  • [LI] R. C. Lacher, Cell-like mappings I, Pacific J. Math., 30 (1969), 717-731.
  • [L2] R. C. Lacher, Cellularity criteria for maps, Michigan Math. J., 17 (1970), 3857ndash396.
  • [L3] R. C. Lacher, k-Sphere Mappings on S2k+], Geometric Topology, Lecture Notes in Mathematics, No.438,Springer-Verlag, Berlin, 1975, 332-335.
  • [P] C. Papakyriakopoulos, On Dehn's lemma and the asphericity of knots, Ann. of Math., 66(1957), 1-26.