Fibered stable compacta have finite homotopy type

Geoghegan, Ross

doi:10.1090/S0002-9939-1978-0515418-4

Fibered stable compacta have finite homotopy type
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Proc. Amer. Math. Soc. 71 (1978), 123-129 Request permission

Erratum: Proc. Amer. Math. Soc. 74 (1979), 391.

Abstract:

It is proved that a fibered compact metric space having the shape of a CW complex has the homotopy type of that complex, and that its Wall obstruction to finiteness is zero.

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The inverse limit of homotopy equivalences between towers of fibrations is a homotopy equivalence-a simple proof