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Fundamental dimension and suspension of approximate fibrations

Authors: P. F. Duvall and L. S. Husch
Journal: Proc. Amer. Math. Soc. 79 (1980), 122-126
MSC: Primary 55P55; Secondary 54C56
MathSciNet review: 560597
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Abstract: Given an approximate fibration $ f:X \to Y$ between ANR's a new approximate fibration Sf is constructed with the property that the fibers of Sf are the suspensions of the fibers of f. This construction is used together with an approximation theorem of T. Chapman to give conditions under which $ {\text{Fd}}\;X = {\text{Fd}}\;Y + {\text{Fd}}\;{f^{ - 1}}(x)$.

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

  • [B1] K. Borsuk, Theory of retracts, Polish Scientific Publishers, Warsaw, 1967. MR 0216473 (35:7306)
  • [B2] -, Theory of shape, Polish Scientific Publishers, Warsaw, 1975. MR 0418088 (54:6132)
  • [C] T. Chapman, Approximating maps into fiber bundles by homeomorphisms (to appear). MR 575307 (82k:57006)
  • [CD1] D. Coram and P. Duvall, Approximate fibrations, Rocky Mountain J. Math. 7 (1977), 275-288. MR 0442921 (56:1296)
  • [CD2] -, Approximate fibrations and a movability condition for maps, Pacific J. Math. 72 (1977), 41-56. MR 0467745 (57:7597)
  • [DNS] J. Dydak, S. Nowak and M. Strok, On the union of two FANR-sets, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 485-489. MR 0413036 (54:1157)
  • [E] R. Edwards, A locally compact ANR is a Hilbert cube manifold factor (to appear).
  • [EG] D. Edwards and R. Geoghegan, Shapes of complexes, ends of manifolds, homotopy limits and the Wall obstruction, Ann. of Math. (2) 101 (1975), 521-535. MR 0375330 (51:11525)
  • [F] S. Ferry, Approximate fibrations with nonfinite fibers, Proc. Amer. Math. Soc. 64 (1977), 335-345. MR 0461505 (57:1490)
  • [N] S. Nowak, On the fundamental dimension of approximately 1-connected compacta, Fund. Math. 89 (1975), 61-79. MR 0377832 (51:14001)
  • [R] F. Raymond, Local triviality for Hurewicz fiberings of manifolds, Topology 3 (1965), 43-57. MR 0159337 (28:2554)
  • [S] J. P. Serre, Homologie singulière des espaces fibrés, Ann. of Math 54 (1951), 425-505. MR 0045386 (13:574g)

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Keywords: Approximate fibration, fundamental dimension, cohomology dimension
Article copyright: © Copyright 1980 American Mathematical Society

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