Pacific Journal of Mathematics

Continuous decompositions into cells of different dimensions.

John J. Walsh and David C. Wilson

Article information

Source
Pacific J. Math., Volume 110, Number 1 (1984), 223-232.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102711114

Mathematical Reviews number (MathSciNet)
MR722752

Zentralblatt MATH identifier
0555.57004

Subjects
Primary: 54B15: Quotient spaces, decompositions
Secondary: 57N99: None of the above, but in this section

Citation

Walsh, John J.; Wilson, David C. Continuous decompositions into cells of different dimensions. Pacific J. Math. 110 (1984), no. 1, 223--232. https://projecteuclid.org/euclid.pjm/1102711114


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References

  • [AnJR. D] Anderson, On monotone interior mappings in the plane, Trans. Amer. Math. Soc, 73 (1952),211-222.
  • [An2] Anderson, Continuous collections of continuous curves in the plane, Proc. Amer. Math. So, 3 (1952),647-657.
  • [Dy] E. Dyer, Continuous collections of decomposable continua on a spherical surface, Proc. Amer. Math. Soc,6 (1955),351-360.
  • [Dy2] E. Dyer, Certain transformations which lower dimension, Ann. of Math., 63 (1956), 15-19.
  • [Dy3] E. Dyer, Regular mappings and dimension, Ann. of Math., 67 (1958), 119-149.
  • [H-W] W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press, Princeton, N. J., 1941.
  • [Jo,] W. Hurewicz and H. Wallman,] W. Hurewicz and H. Wallman,] W. Hurewicz and H. Wallman,] S. Jones, The impossibility of filling En with arcs, Bull. Amer. Math. Soc, 74 (1968), 155-159.
  • [Jo2] W. Hurewicz and H. Wallman, Continuous collections of compact manifolds, Duke Math. J., 37 (1970), 579-587.
  • [Ku] V. I. Kuz'minov, omological dimension theory, Russian Math. Surveys, 23 (1968), no. 5, 1-45.
  • [La] R. C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc, 83 (1977),495-552.
  • [L-W] W. Lewis and J. Walsh, A continuous decomposition of the plane into pseudo-arcs, Houston J. Math., 4 (1978),209-222.
  • [Na] J. Nagata, Modern Dimension Theory, John Wiley and Sons, Inc. New York, N.Y., 1965.
  • [Ro] J. H. Roberts, Collections filling aplane, Duke Math. J., 2 (1936), 10-19.
  • [Sp] E. H. Spanier,Algebraic Topology, McGraw-Hill, New York, 1966.
  • [Wa,] E. H. Spanier,] E. H. Spanier,] E. H. Spanier,] J. J. Walsh, Monotone and open mappings on manifolds. I, Trans. Amer. Math. Soc, 209 (1975),419-432.
  • [Wa2] E. H. Spanier, Light open and open mappings on manifolds. II,Trans. Amer. Math. Soc, 217 (1976),271-284.
  • [Wa3] E. H. Spanier, Isotoping mappings to open mappings, Trans. Amer. Math. Soc, 250 (1979), 121-145.
  • [W-W] J. J. Walsh and D. C. Wilson, The non-existence of continuous decompositions of 3-manifolds into absolute retracts, Houston J. Math., 7 (1981),591-596.
  • [Wi,] J. J. Walsh and D. C. Wilson,] J. J. Walsh and D. C. Wilson,] J. J. Walsh and D. C. Wilson,] D. C. Wilson, Open mappings of the universal curve onto continuous curves, Trans. Amer. Math. Soc, 168 (1972),487-515.
  • [Wi2] J. J. Walsh and D. C. Wilson, Open mappings on manifolds and a counterexample to the Whyburn conjecture, Duke Math. J., 40 (1973), 705-716.