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Transactions of the American Mathematical Society

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Every weak proper homotopy equivalence is weakly properly homotopic to a proper homotopy equivalence


Authors: David A. Edwards and Harold M. Hastings
Journal: Trans. Amer. Math. Soc. 221 (1976), 239-248
MSC: Primary 55D10
DOI: https://doi.org/10.1090/S0002-9947-1976-0410735-3
MathSciNet review: 0410735
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Abstract: We prove that every weak proper homotopy equivalence of $ \sigma $-compact, locally compact Hausdorff spaces is weakly properly homotopic to a proper homotopy equivalence.


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  • [1] E. M. Brown, On the proper homotopy type of simplicial complexes, Lecture Notes in Math., vol. 375, Springer-Verlag, Berlin and New York, 1974. MR 0356041 (50:8513)
  • [2] T. A. Chapman, On some applications of infinite-dimensional manifolds to the theory of shape, Fund. Math. 76 (1972), 181-193. MR 0320997 (47:9530)
  • [3] D. A. Edwards and H. M. Hastings, Čech and Steenrod homotopy theory, with applications to geometric topology, Lecture Notes in Math., Springer-Verlag, Berlin and New York (to appear). MR 0428322 (55:1347)
  • [4] -, Counterexamples to infinite-dimensional Whitehead theorems in pro-homotopy (to appear).
  • [5] F. T. Farrell, L. R. Taylor and J. B. Wagoner, The Whitehead theorem in the proper category, Compositio Math. 27 (1973), 1-23. MR 48 #12545. MR 0334226 (48:12545)
  • [6] L. C. Siebenmann, Infinite simple homotopy types, Nederl. Akad. Wetensch. Proc. Ser. A 73 = Indag. Math. 32 (1970), 479-495. MR 44 #4746. MR 0287542 (44:4746)
  • [7] T. Chapman, All Hilbert cube manifolds are triangulable (to appear). MR 0286138 (44:3352)
  • [8] T. Chapman and L. C. Siebenmann, Finding a boundary for a Hilbert cube manifold (to appear). MR 0425973 (54:13922)
  • [9] M. Mather, Counting homotopy types of manifolds, Topology 4 (1965), 93-94. MR 31 #742; erratum, 35, p. 1577. MR 0176470 (31:742)
  • [10] L. C. Siebenmann, Chapman's classification of shapes-a proof using collapsing, Manuscripta Math. 16 (1975), 373-384. MR 0431183 (55:4185)
  • [11] J. E. West, Mapping cylinders of Hilbert cube factors, General Topology and Appl. 1 (1971), 111-125. MR 44 #5984. MR 0288788 (44:5984)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0410735-3
Keywords: Pro-homotopy theory, proper homotopy theory, Whitehead Theorems, Q-manifolds
Article copyright: © Copyright 1976 American Mathematical Society

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