Covering homotopy properties of maps between C.W. complexes or ANRs

Steinberger, Mark; West, James

doi:10.1090/S0002-9939-1984-0760948-6

Covering homotopy properties of maps between C.W. complexes or ANRs

Authors: Mark Steinberger and James West
Journal: Proc. Amer. Math. Soc. 92 (1984), 573-577
MSC: Primary 55R05; Secondary 54E60, 55M15, 57N20
DOI: https://doi.org/10.1090/S0002-9939-1984-0760948-6
MathSciNet review: 760948
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Abstract: Serre fibrations between C.W. complexes are fibrations in the category of compactly generated weak Hausdorff spaces, but not, by example, in the category of all spaces. Under suitable hypotheses the notions of Dold fibration in the two categories coincide. Examples are given of maps with ANR base, total space and fibres which are not Dold fibrations but whose pullbacks over maps out of locally finite-dimensional paracompact spaces are bundles.

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