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
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by Mark Steinberger and James West PDF

Proc. Amer. Math. Soc. 92 (1984), 573-577 Request permission

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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