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David Roberts ♦
David Roberts ♦
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A short paper with references to several early counterexamples proves that (in the good category of compactly generated weak Hausdorff spaces) a Serre fibration in which the total space and base space are both CW complexes is necessarily a Hurewicz fibration. M. Steinberger and J. West. Covering homotopy properties of maps between CW complexes or ANRs. Proc. Amer. Math. Soc. 92(1984), 573-577.

  • M. Steinberger and J. West. Covering homotopy properties of maps between CW complexes or ANRs. Proc. Amer. Math. Soc. 92 (1984), 573–577, doi:10.1090/S0002-9939-1984-0760948-6.

(The proof is corrected in R. Cauty. Sur les overts des CW-complexes et les fibr'es de SerreSur les overts des CW-complexes et les fibr'es de Serre. Colloquy Math. 6363 (1992), 1--71–7, link). No relationship between the covering map and the CW structures is required. This argues either that counterexamples are pathological or that it is a special property for the total space of a Serre fibration with CW base space to be a CW complex, although it has the homotopy type of a CW complex if the fiber does.

A short paper with references to several early counterexamples proves that (in the good category of compactly generated weak Hausdorff spaces) a Serre fibration in which the total space and base space are both CW complexes is necessarily a Hurewicz fibration. M. Steinberger and J. West. Covering homotopy properties of maps between CW complexes or ANRs. Proc. Amer. Math. Soc. 92(1984), 573-577. (The proof is corrected in R. Cauty. Sur les overts des CW-complexes et les fibr'es de Serre. Colloquy Math. 63(1992), 1--7). No relationship between the covering map and the CW structures is required. This argues either that counterexamples are pathological or that it is a special property for the total space of a Serre fibration with CW base space to be a CW complex, although it has the homotopy type of a CW complex if the fiber does.

A short paper with references to several early counterexamples proves that (in the good category of compactly generated weak Hausdorff spaces) a Serre fibration in which the total space and base space are both CW complexes is necessarily a Hurewicz fibration.

  • M. Steinberger and J. West. Covering homotopy properties of maps between CW complexes or ANRs. Proc. Amer. Math. Soc. 92 (1984), 573–577, doi:10.1090/S0002-9939-1984-0760948-6.

(The proof is corrected in R. Cauty. Sur les overts des CW-complexes et les fibr'es de Serre. Colloquy Math. 63 (1992), 1–7, link). No relationship between the covering map and the CW structures is required. This argues either that counterexamples are pathological or that it is a special property for the total space of a Serre fibration with CW base space to be a CW complex, although it has the homotopy type of a CW complex if the fiber does.

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Peter May
Peter May
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A short paper with references to several early counterexamples proves that (in the good category of compactly generated weak Hausdorff spaces) a Serre fibration in which the total space and base space are both CW complexes is necessarily a Hurewicz fibration. M. Steinberger and J. West. Covering homotopy properties of maps between CW complexes or ANRs. Proc. Amer. Math. Soc. 92(1984), 573-577. (The proof is corrected in R. Cauty. Sur les overts des CW-complexes et les fibr'es de Serre. Colloquy Math. 63(1992), 1--7). No relationship between the covering map and the CW structures is required. This argues either that counterexamples are pathological or that it is a special property for the total space of a Serre fibration with CW base space to be a CW complex, although it has the homotopy type of a CW complex if the fiber does.