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

Edwards, David A.; Hastings, Harold M.

doi:10.1090/S0002-9947-1976-0410735-3

Every weak proper homotopy equivalence is weakly properly homotopic to a proper homotopy equivalence
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by David A. Edwards and Harold M. Hastings PDF

Trans. Amer. Math. Soc. 221 (1976), 239-248 Request permission

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.

References

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David A. Edwards and Harold M. Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Mathematics, Vol. 542, Springer-Verlag, Berlin-New York, 1976. MR 0428322

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