Algebraic Topology · Problem 4K.6

Homotopy Theory — Allen Hatcher

Mathematics — Topology · dold-thom-theorem

Problem

Let XX be a complex of spaces over a Δ\Delta-complex Γ\Gamma, as defined in \S4.G. Show that the natural projection ΔX→Γ\Delta X \to \Gamma is a quasifibration if all the maps in XX associated to edges of Γ\Gamma are weak homotopy equivalences.

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